Start with a free / cheaper application and consider getting a book of Lightroom from the library - if your sensible / cheap
If your wanting to invest in software then Lightroom is better than Photoshop for photographers (certainly for new comers and hobbiests). Photoshop can do more but Lightroom is a photographers piece of software whereas Photoshop (despite the confusing name) is mainly for Graphic Designers.
Ideally, you want to do most of your post processing in Lightroom and the finishing touches in Photoshop CS3 - but thats a lot of money when 80% of the work is generally done in Lightroom.
Lightroom is also easier to use and quicker to learn. Lightroom and Photoshop Elements might be a worth while looking into. Try downloading a trial version of Lightroom and see how you like it.
Google search Lightroom Killer Tips videos because there are some get free video tutorials out there.