I have used Gimp (GNU Image Manipulation Program) for many years - as it is free you can install it on a customer's machine to do quick jobs when on site, and it works fairly well, but at home/work I use Photoshop - if you do enough work, it is well worth the £7.99 (plus VAT) monthly fee. (just get the "photo editing" package)
I have used a free package that came with a DVD drive (may have been part of the Nero suite) - iirc it cost less than £15 to buy the DVD drive and the software came free...
My late wife did a few videos with Microsoft's free package called Movie Maker - And I must say, her videos looked better than mine - not sure if it was the software, or the talent of the operator
As to computer "Power" - Gimp will work on most computers fairly well - Photoshop is a bit of a power hog..
When editing video, your temporary files can get big, so a quick hard drive is a big bonus and SSDs are really coming down in price now.
As an example, I have just bought a second hand Quad-core Xeon with 8Gb of ram and a FireGL graphics card for re-sale to a customer (no hard drive) for £120 - Add a 240Gb SSD for around £80 and you have a lot of bang for your buck.