Agree on going with safty razors, but once you are there, you don't want to cheep out. The one option my local grocery store carries is a $20 that is complete junk. I invested $70 in a Henson safty razor and never looked back. They also have a $250 offering for people who want the benefits of a safty razor without the cost savings.
For blades, I actually splurge and buy the $0.20/piece offering from Feather instead of the $0.10/piece ones that Henson sells. Still cheeper than the $0.80 safty blades the grocery store sells, or the checks app $4.50/piece cartridge blades the store sells?!?
Moral of the story: go cheap, but don't be afraid of spending a little money to do so.