While the OP's original project must be long finished by now, let me write an answer from the perspective of a similarly beginning hobbyist who's just been through the learning curve (also, I think some things have changed in just the few years since the original question):
First, there are now several cheap PCB prototype manufacturers, a list of which you can find at pcbshopper.com, and in addition to those I'd mention Hackvana, which I've tried once and had a good experience with. Up to 4 layers is not ridiculously expensive anymore, and also delivery times a bit less than two weeks are affordable (although the cheapest is still 2 layers and a month for delivery).
For software, you can use anything which exports gerbers. I personally recommend KiCad, which has a slightly idiosyncratic UI but perfectly usable once you get used to it, and most importantly, since it's free and open source, there is no danger of vendor lock-in. For comparison, I find the interface more logical than Eagle.
As far as soldering goes, a temperature controlled iron with a good tip, and a lot of flux for multi-pin packages, goes a long way. A beginner hobbyist, I've now built five boards (with the last two self-designed), going from through-hole to 0.5mm pitch LQFP SMD's and 0603 passives in that time, and I seem to be doing fine enough. Watch the various soldering tutorials, practice on some kits, and you should be fine. Just to point out that to start with I was the most hopeless case you can have: back in school I was the kid whose any product in woodworking class was just a piece of wood inside a blob of glue (and metalwork just resulted in me burning myself...), so you don't need to have special craftsman skills to learn SMD soldering to a usable level.
However, I don't have experience with the QFP's the OP mentions, although I expect that with a hot air station it should be doable. Those are not too expensive these days, although watch out for the very cheapest ones.
To summarize: for a hobbyist, the process these days is:
- choose an EDA software that suits you, as long as it exports Gerbers, and learn to use it.
- draw your schematic and route your PCB
- pick a cheap PCB prototyping service you like, and send the Gerbers to them
- Solder the board. Don't be too afraid, it's easier than it looks, you'll just need to be careful and concentrate.