Sony Acid is what you're looking for.
It has a "beat mapping" facility". It reads the beats in all your files, and then when you're using a "computeriesd" fixed tempo beat it should align properly once your tempo is set....or with very minor editing....(assuming the songs you're using don't vary in tempo wildly!).
Acid is the software that most mashers used to use....many now have progressed to Ableton or others, but for a relative beginner, Acid is excellent. It will take you time to get used to using it....don't expect to be producing "the finished article" in 5 minutes! However, once you've sussed it out....well, i've said it before, a 5 year old could use Acid and produce something nice.
There are fully capable trial versions of Acid available.....
http://www.sonycreativesoftware.com/acidpro .
You should be able to find older versions (non-trial) at torrent sites.
Somehere on the Sony sites you'll also find lots of free sample packs that you''ll find very useful....drum loops etc, that you can use in your mixes. Build up a library, they're invaluable.
Personally i don't use Acid...(LOL)...I used it for a while a couple of years ago, and found it to be pefectly capable.
The first mash ups that i made that i would consider to be "perfect" were made using Acid.
But....i started out using Adobe Audition (well...CoolEdit 2 it's earlier incarnation actually)....and the way it works is different to Acid, so i was always working "backwards"., so i migrated back to Audition.
Audition is a super multi-track Audio editor, but it lacks the beat mapping capabilities of Acid. All my synchronisations are done manually.
So...give Acid a try.
Also, seek help from the guys who know. If you go over to GYBO ....
http://www.gybo5.com/index.php?option=c ... a&Itemid=3 you'll not only find some great music, but also great resources.
These guys are the "pro's". They have a huge knowledge base and are very helpful. They should be able to help you with Acid questions and general help.
Good luck.
Andy.