#3 - Players typically purchase their starting gear from the gold they are given at first level. The SRD has a great article on character creation, and equipment is under section 8. The gold you have listed is, according to the SRD, actually the average for each class. As a DM, you can choose to give them the average for first level, or make them roll.

It would be good for them to look at the pre-bought sets the describe, so they can understand what's typically needed. Once they get more comfortable, they may branch out according to how they like to play their character.

Of course, as the DM you may overrule this and force them to start with a certain set of items, or give them more gold, etc. Seeing as this is your first time playing, however, I highly suggest sticking to rules as written since this sort of overruling may very well have unintended side effects.

As an aside, wizards get so little at first level because they don't need (and cannot wear) armor, nor do they need expensive weapons like swords and bows.

There are a number of good ways to do this. Both of the non-crafting ways you mentioned are actually perfectly good ways of going about this if approached properly. I will detail them in the order you should attempt them below:

Buy it in the store

By the book

If you want something and don't have it, the normal way of procuring it for most people in modern societies is to buy it. If the item you want is more commonly available than normal in your GM's campaign (I'm guessing capes of the mountebank aren't unless all items under a certain price are), you might be able to pick it up from just about anywhere. In both D&D 3.5 and pathfinder, there are guidelines for the kinds of magic items normally available in a settlement based off of an item's price and its classification and minor, medium, or major. A cape of the mountebank costs 10800 gp and is a Medium Wondrous Item in both D&D 3.5 and Pathfinder.

In Pathfinder, that means you can theoretically buy it in a village if you're lucky enough to roll it as one of the 1d4 random medium magic items for sale (or travel through a lot of villages). Bigger cities will have more items of the right level, but there are a huge number of items so it's somewhat unlikely that yours will be randomly rolled. Otherwise, you'll need to find a metropolis to be sure you can purchase your cape, as only settlements of that size have a base value over the price of your cape. The cape has a 75% chance of being available in such situations, which you can roll once each week. There are various traits (like dealmaker) and other character options that can effect this, but it is unlikely you have any.

In D&D 3.5, things are simpler as the 'GP limit' of a settlement applies both to buying and selling of goods and things are always available below the limit and never available above it (unless GM shenanigans are afoot!). Consulting pg. 137 of the DMG you can pick up your cape from the nearest small city or larger settlement.

Working like a team

You really should talk to your GM, though. The best way to do this is in character: ask around town about the item your looking for and maybe put an offer up on the tavern's quest board or other place to post desired items. When a merchant says he can't get you that item, ask if he'd be able to special order it (maybe offering a 10% bonus for his help) and, if he declines, ask to be directed to someone who can. Make sure you put your postings up in every town you visit so that word gets around you're looking rather than staying in one place, and be sure to leave directions as to how to contact you or some agent of yours capable of making the deal. Generally, if you have the money, you can acquire the item you want after a few months of time in worlds modeled after old-school D&D, while in newer worlds items are easier to acquire unless forbidden by GM fiat. Often, especially with new-school GMs, the GM will be excited that you are hiring an NPC merchant to do cool merchant-y things (even more especially if the NPC was an ally from a quest you completed. If you recently saved a caravan, getting them to do this for you during their travels is very likely to be successful even with GMs who rarely allow magic items) and pay off your role-playing with faster service, an exceptionally high-quality item, or a discount. Be sure to use divination and communication magic if you or a party member has access to any, that is what it's for after all.

Make it or have it made

Flying Solo

If you can't buy the things you want, presumably because they're not for sale anywhere you can find and you've already tried the above suggestions, making some yourself or having some made for you becomes a good option. As a ranger, you ARE a spellcaster, though you almost certainly lack the feats you'd need to craft a wondrous item and taking them would be prohibitive unless you want to craft lots of items. Crafting also takes a time; your cape will take a base time of 11 days in both systems. In D&D 3.5 you will also lose 403 XP if you craft the item. It is more GP efficient, though, and you will be able to get the item for half of what you would otherwise pay.

Like a Vampire Bat: Reciprocal Altruism at Work

Probably, then, you don't want to craft the item yourself. Instead, find an appropriately leveled bard, wizard, sorcerer, witch, magus, travel domain cleric, or summoner (pathfinder), or an assassin, bard, travel domain cleric, sorcerer, or wizard (D&D 3.5) willing to craft the item for you and pay them to do so. You should be able to find such a person by asking around and advertising just as you did for the item, though you want want to frequent different places and social networks as appropriate.

"Talk to the GM" aka Goin' on an Adventure

Library, Ho!

At this point, you've tried buying the things you want only to find that not only are none currently for sale, no one alive today can produce one. Your Cape of the Mountebank must be pretty special. Luckily for you, you live in a medieval fantasy world, where the past is often more advanced than the present and Indiana Jones style archaeology produces most of the GDP in most of the world. It's time to crawl some dungeons, but first you need to find the right dungeon to crawl. Talk to sages, diviners of epic power, and your local bartender to find the location of a long-lost Cape of the Mountebank, or, at least, a library or other place you could find such information. At this point, Legend Lore is your best friend and, if you have it, you can probably get your next adventure to net you your cape.

Don't Damage the Goods

While Nuclear Fireball, Summon Sphere of Annihilation, and Mordenkainen's Permanent Destruction all sound like fun spells (disclaimer: they may not exist) you should not use them, or any spell or effect that sounds like them, while crawling for your now legendary Cape of the Mountebank. Massively destructive effects, especially those which target magic or magic items in specific, might destroy the very thing you've spent so long tracking down. Stick to single target or non-object-damaging effects (or your weapons in your case, ranger) to avoid an unfortunate accident.

Of course, if all else fails, you could use a Wish... (but it's above the listed ok price in 3.5 and Wishing for magic items was removed from the safe list in Pathfinder so you'll probably end up dead or otherwise screwed over if you do)