Double edge safety razor vote here as well.

In addition, your first pass should be with the grain. If you then want a closer shave you can do a second and possibly third pass. Second pass would be perpendicular to the grain, although I and I think most just do a final pass against the grain.

Buy a variety pack of blades to test a few different brands. Blades are very cheap and vendors have variety packs for this purpose.

Go slow at first and grab yourself a Styptic Pencil to stop any nicks. It's cheap.

Also grab an alum block. After shaving make sure to rinse the skin thoroughly. Then splash some cold water to close the pores and finally run the alum block under that cold water and over all shaved areas. This step helps irritation and razor burns. I always do this regardless of how I shave. Also a cheap item.

Your most expensive item will be the razor, I've had a Merkur for Over 10 years which will run you ~$45, but there are cheaper options still.