Photoshop is a must - but when I first started using it 7 years ago I found it hard to get into. Now, it's a doddle.
I'm not familiar with Lightroom, but also heard that's just as good for processing images.
There is a free option out there for users. It's called GIMP. Heard a lot of good reviews on it to say that it's free, but I've personally never used it.
If you want to get Photoshop, you may find that you can pick up an older version for less money in the shops or on ebay. In my opinion I always found Photoshop 7 to be pretty good!! The newer CS versions are good, but oldskool is always better. I've been using CS4 for the last few months and I don't particularly like it compared to earlier CS versions.
If you've not got any editing programs, try GIMP first for free. See how you get on, if its not fulfilling your needs then start to look into Paid for programmes.