If you're really new to this, you have a couple of choices in setting up an online store.
You can go with something like Yahoo Stores, where it's pretty much all point and click. There are a number of other hosts, such as GoDaddy and 1&1 and others, which also offer "easy set up" stores that don't require you to know much of anything about HTML or programming. It's just a matter of checking them out and picking the one you feel most comfortable with.
The advantages to this are: you can get going quickly, it's relatively easy to get started and you'll have relatively few expenses out-of-pocket up front beyond the basic hosting account. The main disadvantages are: it's probably going to be more expensive over the long run (the hosting companies usually charge extra per month for store accounts versus basic hosting accounts) and -- depending on the store -- it may be tricky to migrate your data to another store platform should you one day outgrow the one you're on, and (depending on which one you select) you may be somewhat limited in your design choices (at least until you learn HTML and CSS enough to code a custom template, assuming the store allows custom templates).
You can hire somebody to set up a store for you. This will definitely be more expensive up-front and will take more time than using one of those "be online by tonight" point-and-click services I mentioned above. But on the other hand, you can get your store totally customized to your specifications and your monthly outlay going forward may be somewhat less.
Of course, you could always teach yourself and try to DIY, but unless you already have a bit of background in HTML, web design and (potentially) programming and/or server administration, I wouldn't necessarily advise that for someone just starting out with e-commerce. Not to say that it can't be done, or that you couldn't pull it off very well, but you are facing a significant learning curve. If you have the time and the desire, it's certainly a viable option.
As to knowing whether vendors are reliable or not, you can try searching for the vendor's name plus words like "sucks" or "complaint", and see what comes up in the results. Keep in mind, almost any vendor will have a complaint or two, so I wouldn't panic over a small number of negative entries. But if you see entire websites devoted to how terrible the vendor is, with post after post from all sorts of different people, that would be a huge red flag.
Of course, it's possible the vendor is new and hasn't had a chance to build up an online reputation yet. Best advice I know of is to start small, build up gradually and always always always have a backup plan (and if you're as paranoid as I am, a backup of the backup
As to drop shipping versus stocking, that's a business decision that will vary from one person to the next. There is no one "best" answer that fits all.
From the standpoint of warehousing and shipping yourself: do you have enough space to warehouse these products? Will you be available every day to ship out orders, or will your customers be willing to accept a few days' delay on shipping if you're away on vacation or ill, or will you have employee(s) who can take over shipping duties when you're not available?
On the drop shipping side, are you comfortable with the quality of the products and the packing/shipping by your drop shipper, such that you're okay with them sending products directly to your customers? Are you confident they'll ship on a timely basis? Do you trust them to not "poach" your customers?
If you can price the products enough to cover a small additional cost and still give you sufficient profit, a compromise might be to use a fulfillment house. They warehouse and ship the products on your behalf, so you don't have to be around all the time, but they're not a manufacturer or distributor on their own, so there's less worry about them making use of your customer list to sell their own products directly.
Hope this helps!