Chris:
1- Your are right that for photo editing you need a Right
computer first but if you are a patient person and I know you are, even a 5 years old computer (Every computer year is equivalent of 20 to 25 human year), is still good enough.
2- There is no substitution for
Photoshop, lets put it this way, PS is the equivalent of English language for a traveler; You can talk to most people that way.
3- If you really need a substitute that wont cost an arm and foot, think of
Corel paint shop pro. I used it when I was in need of CA (Chromatic aberration) removal when PS would not give me that option. I did the 30 days free trial that I found to be a very very effective program, being offered for a fraction of cost of others. Here is a link and this is a newer generation that is on sale now for $59, so consider this as a gift from me

here is the
L I N K
4- Free Picasa that is given by google is a program that needs admiration as well. It was my introduction to software use for post processing and I found it to be a very useful elementary level program. Still if in need of sending a lot of picture via email, I prefer its use that is so easy.
5- At times when you buy the right old computer, you may land up with treasure of softwares on the HD, of course I am not sure about the legits of their questionable third party use.
Hope this helped.