I'm going to separate it by budget, because most beginners know that right off the bat.
These are the three major kinds of discs that you can expect to work with. They'll give you a great base to begin figuring out what you like best.
I use my fairway driver a LOT (because the holes down at Johnson St are short-ish), even though I have a longer driver. Any of these drivers you purchase will definitely be usable for a long time even as you improve. All of these are nice and straight and will help you learn good form.
The Cobra and Stingray are not technically drivers, but work well in that role for beginners and also for holes where you are over-throwing the hole with a regular driver. And as your technique improves, it will still have a place in your bag. And because of it's narrower lip/edge, it is easier to throw for folks with smaller hands. But I have big hands, and I throw it just fine, too.
For your Putter, just find one that feels like it would be good to throw. The Magnet and Aviar are very popular. Some will say "soft" on them and you may notice that they have a little tackier feel. They are intentionally that way because some people think the softer surface "grabs" the chains better than a harder surface. Often, you'll find a normal version, and a "soft" version of the same disc. I like the soft ones, but some play with the "not soft" ones. I would stay away from the harder plastics ("pro", "champion", "X", "Z" -- basically get the cheap one and you'll be good), though.
The goal here is to get one disc that can do a little bit of everything. In the beginning, you'll probably be able to throw a mid-range just as far as you could throw a driver. I know that was the case for me.
Of the discs listed above, either of the two Discraft discs are better choices for beginners. However, all the discs above are good mid-range discs. They also are highly regarded enough so that when you gain more skill, these will still have a place in your arsenal.
* The Comet comes highly recommended, with one reputable source saying that it's one of the best beginner discs available. But I haven't used it yet.
What your disc is made of will govern how expensive it is. Most disc molds/models are available in a few different plastics.
Not-As-Hard Plastics - The cheapest. They get worn in quicker. You think, "I don't want to get the cheapest." But in this case, you probably do. They are easier for beginners to throw well. They can cost $6-8 each. Because they are so cheap, it's great to experiment with them to find what you like. And if you lose it, due to a crappy beginner throw, you haven't wasted as much money. Innova calls theirs "DX" and Discraft calls theirs "D".
Hard Plastics - Innova calls theirs "Champion", "Pro", or "Star". Discraft calls theirs "X" and "Z". These usually cost $15 or so. They are more resilient to damage, but are a little harder for beginners to throw well.
The flight characteristics of any given disc will vary depending on the plastic from which it's made. In other words, a Cobra made in DX plastic will fly differently than a Cobra made in Champion plastic. The difference is not great, but is noticeable. So if you spend your time pouring over the stats for a DX Leopard (for instance), know that path will probably be different than the Champion Leopard that may look cool in the store.
Disc weight is important. Discs that are lighter are easier for beginners to release properly. Lighter discs are also more tolerant of technique errors and will fly better than their heavier counterparts.
The lightest discs are around 150 grams. The heaviest are around 175 grams. The underside of the disc should have the weight in grams. Sometimes it will be written in pen in the center of the disc. Sometimes it will be on the inside edge or on a small label.
Also keep in mind that as a beginner, you'll probably be tromping through the woods looking for your disc. A disc that contrasts with leaves and dirt can be much easier to find. Whereas a black or dark purple disc will be harder to find.
I began playing in the late winter, when there were no leaves except the brown ones on the ground. Therefore, I learned that yellow discs were very easily spotted. So I've made yellow one of my primary disc colors.
However, I've learned that during the late spring and summer, the yellow doesn't stand out as much as it used to. The bright sun and the way it shines on the green leaves make it harder to find my yellow discs than before.
There are some tie-dyed discs out there as well. They are usually more expensive. I think they would also be harder to find if you pitched it off into the woods.
Colors I'm going with now are more in the orange, red, white, and blue hues.
When you buy discs, you may see some white discs that say glow on them. Yep, they glow in the dark. They are used for night games.