What's the easiest/cheapest way to replace my battery? 2009 MBP
Having recently done this for a colleague, I can answer in the affirmative that there are excellent 3rd party battery suppliers for this particular model MacBook Pro and they are quite easy to replace.

I used the Lizone battery mainly for it's high ratings on Amazon and the fact it came with an 18 month warranty (better than Apple's 1 year warranty).

Replacement was super easy.  There is a guide on ifixit.com but I didn't really need it.  I just removed the back cover, removed the screws holding the battery and used a plastic pry tool to gently pry the battery loose from the adhesive.  Installation was simply the reverse procedure.

Since I had everything opened, I maxed out the memory with 8GB of RAM and added a Samsung EVO SSD.  While I am partial to Samsung, PNY and Crucial are also very good brands.  Basically, any 2.5" SSD will work in this MacBook so pick one that you like the best.

It's important to note that the SATA interface of this particular MBP is SATA II (3GB /s transfer rate).  If you can get a SATA II drive, it will work just fine.  SATA III is backwards compatible, but you won't see increased speeds above the 3GB /s transfer rate.