I agree with Donoreo and John. If you're just starting out then Elements is the way to go.
Cost is a major factor in any software procurement. Photoshop CS is about £600 while Elements 10 can be found for as little as £57. Bizarrely, Amazon are selling E9 for more than E10.
I don't know anything about Lightroom other than it comes in around £100, but a lot of people like it.
Again, Topaz is a mystery to me. But I understand that it's a plug-in to Photoshop anyway. So, you'll need to go that way first.
If you want something that is reasonably powerful and, crucially, FREE. You should have a go at Gimp or Photofiltre. You won't find much in the way of tutorials in magazines but they're fairly intuitive and there's a heap of people out there using them and you should be able find a few on this forum.