as far as final cut vs after effects: they are both non-linear editors (unlike imovie & Premiere, which are linear, ie you edit the movie beginning to end, scrolling/scrubbing along the timeline), so take that into consideration. i prefer linear. after effects is meant for doing what it is named: adding effects, but also functions as a movie editor. so unless you plan on doing fancy digital alterations, i'd stick to final cut or premiere.
First off this is wrong. Premiere and iMovie are both NLE's as well. Linear editing would be something like tape to tape and is pretty much dead, not something you would be using with a digital camera.
As for my opinion of software It really depends on what you want to do and how far you want to go in the industry. I would learn FCS 3 first. Any job you apply for will ask if you know that first and it's a great place to start. Learn everything from motion to color and soundtrack pro as they are still the industry standards. FCP X is junk, but there are lots of rumors floating around that upgrades are coming and it will regain its place on top of the NLE throne. One small annoyance if you are using DSLR footage is you will have to transcode all of it to apple prores through a program like mpegstream clip. Not a major problem just an extra step in the workflow.
Next is Avid which is another one of the top NLE's out there. I don't have much experience with it but it has been the number two program for quite a while. A lot of companies will ask if you know this as well but as long as you know final cut you should be good to go.
Last is premiere pro. It is easily my favorite of the three. It's mercury playback engine and dynamic linking have made my life much easier, especially working with DSLR footage. Before CS5 came out it was never quite right but CS5 and after are amazing. Not having to render or transcode every bit of footage is amazing. just being able to plug drop and go is amazing. You can export as an XML even if you need to use FCP or anything like that ( I use it for plural eyes all the time). It even links up with Avid im pretty sure but ive never used it. You can even set all the hot keys up to be the same as FCP. It could become the new industry standard and there has definitely been a shift in that direction but I would still say more people use the old FCP. My office is still split 50/50 on what people would rather use. I was very hesitant to switch over but about a year ago I did and havent done a personal project in FCP since. My office did some beta testing for cs6 and being able to use warp stabilzer right in premiere is amazing especially with dslr footage. I used that with a glidecam shoot i had last week and it made me look like a pro even though I still not very good with a glidecam.
While After effects can be used as a NLE it should only really be used for composting and motion graphics. It is simply slower and not built to handle footage like FCP or Premiere are. I would definitely recommend learning it though somewhere down the line for some project you will want to do some fancy effects and it is the best.
After that there are still all sorts programs ranging from 3d to color grading to sound and each of them will have pros and cons for each of them but I would recommend learning basic NLE first unless you really want to go into one of those fields.
For a computer I would look into refurbished macs. they tend to be pretty cheap and usually have some great parts. I use a 3 year old 17" MBP and it handles most things prety well. anything short of 3d animations or a real heavy after effects file and i never have many problems. granted when I work on other computers it renders out faster but on mine I can still play back native footage in real time as long as i turn the quality down a little bit. If you can find a 15" with thunderbolt that would be the way to go. If not just buy a couple big firewire externals and edit off of those. You could also go the PC route. One of my good friends who is an after effects genius swears by his pc. I don't know a whole lot about them as I have been using macs for quite a while now since I had to run FCP. But beware if you do you go the PC route Macs are again what most of the industry uses. Every job I've had we have used macs (but then again we all use FCP too so that might change).
Sorry this is really long and rambley im just writing things as the come to me and if you dont feel like reading it all just get a 15" MBP with 4gb of ram and a 2.5ghz processor and a copy of FCP7 and that will be a great starting place.
Edit: just saw you sent me a pm dylan. I will get to that when I have a chance.