Run Death House
Death House serves much better as an introduction to CoS over Phandelver. Phandelver is a great adventure, and I started as a player with it, but it would serve you better later if you want to run a classic D&D adventure, with less gothic horror elements. I'm DMing Curse of Strahd now and started my group with Death House.
Death House will teach you certain DM skills, and it will reinforce the skills necessary for the PCs to survive Curse of Strahd. Here's my justification:
Introduce with Roleplay and dread
Curse of Strahd is a roleplay-heavy campaign — there are lots of situations you don't want to bash your way through. Additionally, Death House will, if played correctly, teach you as DM to foreshadow threats and create a sense of dread that will help with the rest of the campaign on both sides of the table.
For example, the desolate streets of Barovia, with only a single house on the outskirts lit up, with smoke pouring out of the chimneys will draw the players in, but also give them the eerie feeling something is wrong. You'll have to play the children correctly to bait the players in, but you can always use the mists to railroad them as necessary. Once they're in the house, you'll be able to hook them in.
This introduction is much more in-line with the tone and nature of the rest of the campaign.
Take time to describe the environment
This is critical with Death House, but less emphasized with Phandelver. With Death House, you'll need to take time in each room, describing the blazing hearths, the strange wolf-helm armor, everything. It's all important, because it also teaches the players to pay attention to the environment. When
the blazing hearths pour out poison smoke in the 2nd phase,
they'll get a good idea of how Barovia works. You'll have plenty of chances to have them roll Investigation, Perception, and Insight during the buildup, and therefore teach them some fundamental rules, and fundamental survival skills for later.
Toss a bit of combat in after
The first fight will likely occur later,
on the 3rd floor.
This will be after the players have had the run of the house for a bit, and will give you plenty of time to switch from warm, but empty house, to
the dusty, old, decrepit 3rd floor.
Using that buildup, when something bad happens like
the armored statue punching a player in the face,
the players will be alert to such changes. It's also an easy fight to run, but will introduce damage resistance and basic combat rules.
Phandelver starts you off with a goblin ambush, which is fine, but Curse of Strahd places the emphasis on the fact that the players can walk into dangerous areas — Phandelver's goblin ambush is more of a device used to spur the plot along (perhaps much like the mists). Death House will give you a chance to explore first. Having the combat after emphasizes where the priorities should be in this campaign, I think.
Ramp up the danger
Death House is notorious for how lethal it can get — your players can absolutely TPK against
the Shadows, or the Shambling Mound in the basement.
However, much of the campaign is like this — you'll get to make the decision of how hard to beat them over the head with their impending doom, or how to fail forward. You'll learn from your players what they expect out of a campaign with this kind of tone, and it'll get everyone on the same basis. Starting with Phandelver, I think you stand the danger of letting them be the big damn heroes and then taking that away from them.
This could go a number of ways, depending on how you rule it. I'll address the problems first.
What is an Object?
First and foremost, you have to consider what the definition of an Object is. The Minor Conjuration feature says...
[...]you can use your action to conjure up an inanimate object [...] no larger than 3 feet on a side and weigh no more than 10 pounds, and its form must be that of a nonmagical object that you have seen.
Herein lies the first problem. Is a blob of Fusile Hydrogen an object? Is it discrete enough that it is an 'object [he] has seen?'
The DMG (p.246) defines an Object as such:
[...]an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone--not a building or a vehicle that is composed of many other objects.
By interpretation of this rule, no. It would not be. But, as a DM, this is still your call.
This also raises the question of "Can you conjure Part of an object, or only whole objects?" For example, could you conjure a chunk of a ship, because you've seen a ship before?
Is the Sun Magical?
In many realms, the sun is magical in nature. It's not a ball of fusing hydrogen...it's either a deity, or a hole in the fabric of the sky, or a massive portal to the Elemental Plane of Fire, or something else entirely. If the sun is magical, then he can't summon parts of it.
Assuming you're going to let this happen....
(Note: This section has been rewritten after errors in an equation I was using were pointed out to me. This altered the output of this answer dramatically)
If he summons a chunk of the sun, and assuming the sun is similar to our sun:
He can conjure a maximum of just over 30 cubic centimeters of solar core (a block about 3.1 cm to a side). This is because the Solar Core has a density of 150 grams per cubic centimeter, and Minor Conjuration can only create 10 lbs of matter (appx 4536g). This block of matter is held at a pressure of 26.5 Petapascals and a temperature of 15 million degrees C.
This seems absurd...but remember that this is a tiny piece of matter that is going to hurl itself apart the moment it is conjured (again, further evidence for it NOT being an Object). The amount of time it takes for that tiny wad of plasma to disperse would be extremely short. But, let's see what this does anyway.
While the sun's typical energy production is low (276.5 W/m3), that is still a lot of thermal energy that needs to go somewhere.
From here, it's time to break out the math. For simplicity's sake, we're going to assume the plasma behaves like an Ideal Gas. Because otherwise this gets completely insane. So, to determine the total available energy of 3ccs of solar matter, we can use this equation:
$$E = {\frac{3}{2}nRT}$$
Where E is energy, n is the number of moles of gas, R is the Gas Constant, and T is the temperature in Kelvin. At this scale, the difference between Celsius and Kelvin (273.15 degrees) is basically negligible.
At the heart of the sun, the composition is roughly 33% Hydrogen, 65% Helium, 2% Other. To determine how many moles we have, we're going to ignore the '2% other' (again, for sanity's sake) and just consider 33% Hydrogen, then just wave my hands and say the other 67% is Helium. Not strictly accurate, but close enough for my purposes.
So, starting with a total mass of 10lbs (4535.92g), we have 1496.9 grams of Hydrogen at 1.008 g/mole, and 3039 grams of Helium at 4.003 g/mole. This gives us a total of 1485 moles of Hydrogen and 759 moles of Helium. Total moles of matter: 2244
So, plugging in the numbers
$$E = 1.5 \times 2244\text{mol} \times 8.31\text{J/K} \times 150,000,000\text{K}$$
For a result of 4,195,719,000,000 Joules or 4.2 Terajoules
This is going to be a VERY large explosion. We aren't reaching the range of a nuke yet...but let's get some comparisons.
If every drop of fuel in a Boeing 747 went up at once, it would unleash 6.4 Terajoules. 12 Terajoules is what would be imparted to you if the International Space Station rammed you. 63 Terajoules (15x our drop of solar matter) was the Little Boy Atomic Bomb.
This is going to be an enormous explosion. Again, if you are permissive enough to allow that part of a star, an amorphous blob of highly dense, extremely energetic plasma, counts as an Object.
I would also mention...if you let a player conjure 'plasma' as an object...don't be surprised if they start trying to conjure up acids, toxic gases, and other amorphous substances.
But how many dice is that?
Per request of a comment, I will now attempt to render this blast in terms of dice of damage. Disclaimer: I am now applying physics to D&D rules. This segment is for entertainment purposes only (because anything caught in such a blast is dead anyway).
Tests conducted on medieval melee weapons show that a typical 1-handed swing of a Mace imparts about 130 Joules to a target. In D&D 5e, a mace deals 1d6 damage. So, to compute the dice of damage of direct exposure to the heart of a star, let's just assume damage scales linearly.
Our little spoonful of sunshine unleashed 4,195,719,000,000 Joules of energy. Divide by 130...
32,274,761,538 d6 of Fire Damage or, put simply, 32 giga-d6.
Best Answer
That's a valid route.
But it's still not easy. You've got to get from location 38 to location 32 in the basement (assuming you even know location 32 exists). Once you're there it's clear from the text that the trapdoor is intended to allow movement from the basement into the house proper.
Then when you're up in the house you're in a poisonous-smoke filled room whose walls will burst with rats when you try to hack through them. It's a shortcut, but no cake-walk.
Welcome to Barovia.