You're going to get a variety of opinion here, most will guide you to spending money on a vise and tools, then build your materials stash as you start working on different patterns. The advantage here is that you start out with a vise and tools that can be of a higher quality than what is typically found in a kit. The materials in a kit more often than not are not high quality and thus making tying flies a little bit more challenging. Believe it or not, the materials can make a difference, not only in the outcome/durability of the fly but actually tying can be easier with higher quality materials. Hackle and Peacock Herl come to mind as two examples.
The other school of thought is to buy a kit as you seem to be leaning towards. I seem to recall in another thread that the Orvis Tying kit was highly recommended. I have not looked at these but again, seem to recall people who are better in touch with the industry recommending this option.
This is a very good read, recommend that you take a look though this before deciding. Edit: Looks like FISHN and I are on the same page, right on FISHN!
Again, you're going to see a lot of opinion here and I'll offer mine. First, establish what you think is a reasonable budget. If you have a local fly shop, go there and see what they have to offer and let them know what your budget is. If you end up buying there, you can establish a relationship with the owners/workers and gain valuable knowledge that you won't get from a big box store. Tips on local patterns, how to's, etc are invaluable. This is the most desirable option IMHO.
If a local shop is not an option, then you're back to kit vs. buying in pieces. Something to keep in mind...if you purchase a kit and don't like it, it may be harder to sell. A more desirable vise and tools will be easier to move if you don't stick with it. You seem to have enthusiasm for tying, which is great! Everybody upgrades at some point. I started with a kit which I received as a gift. I still think of this as one of the best gifts I've ever received in fact. With that said, I have upgraded so I sunk more into tools, vise included after the fact.
Ask yourself if this is something you think you will stick with. If yes then I'd go the vise & tool separate option. You'll have something you can tie on for a while and not have to spend money on that stuff again. If you are unsure, the kit option gets you into tying with less of an investment.
Good luck let us know what you decide upon.