You have it all basically correct
So I can prepare wisdom mod (lets say +3) + level per "instance" (before doing a long rest). (So I can prepare 6 spells)
Yes, you would have 6 spells prepared each day. However, you get your spell slots back and you get to re-prepare spells after a long rest, not before. You would need to complete the entire long rest before you prepared new spells and got your used spell slots back.
I can choose any 6 spells out of the level 1 and 2 list (since I only have level 1 and 2 spell slots)
Yes, there are no restrictions on which spells you can prepare, so you can prepare all level 1 spells, all level 2 spells (although that isn't a very good idea with only 2 level 2 slots), or any combination of the above.
I can cast the same spell as MANY times as I want (like I can cast goodberry (a lvl 1 spell) technically 6 times (4 level 1 spell slots, and 2 level 2 spell slots). The level 2 slots will increase the damage of course.
Mostly correct. Not every spell increases in potency when cast at a higher level. In fact, the Goodberry spell you mentioned does not get any better when cast using a level 2 spell slot. Many do, but some do not. Keep that in mind and make sure to read the spell description before you use it in a higher level. To be clear, you absolutely CAN cast a low level spell in a higher level slot, however if there is no additional benefit for casting the spell in a higher level slot (as per the spell description) then you may not be optimally using your limited spell slot resources.
but I could only cast spike growth (a level 2 spell) 2 times, because I cannot cast it as a level 1 spell.
Exactly.
I could do a long rest and re-prepare 6 more spells and my spell slots would all be refreshed.
Yes, with one minor caveat. Keep in mind that Rules-As-Written, it is not the player that decides to take a long rest, but the DM/GM that decides if a long rest is available. Make sure you know how your DM is running the game, because you cannot initiate a long rest without DM approval, and that may determine how you use your spells and which spells you prepare.
Best Answer
When you level, the number of prepared spells you'll have will increase, but you still only prepare specific spells after a long rest, as normal
You are correct, the total number of prepared spells available for druids are Druid Level + Wisdom Modifier. So when you level up, the total number of prepared spells will increase, either just by one (the level increase), or by more (If you get an attribute point increase with your level up, which increases your wisdom modifier).
However, you pick which spells are prepared after a long rest. So even though you have leveled up, and tracked every other benefit to leveling up, you still have to take a long rest to replenish your spells and prepare new spells (or keep the spells you had prepared since your last rest). This also means that you can prepare a whole new set of spells after another long rest. The only restriction is that you have to prepare all of your spells at one time, and only after a long rest.
To answer your last question, the total number of spells prepared is for all of your spells, chosen from the entire Druid spell list. You can only prepare spells that from spell levels you are able to cast. (For example, if the highest spell level you can cast is level 4, you cannot prepare any spell level 5 spells). You still follow the number of spell slots per level for each spell level according to your character level.
So you may be able to prepare say, 10 spells total. But you can only cast 4x level one spells, 3x level 2, 2x level 3 spells, etc., or how many it says under your character level on the druid level chart in the PHB.