My 160 won't drop into gear all the time. It's become fussy I guess. My question is, is it a clutch I can replace, or a transmission? When I engage the clutch peddle, sometimes it works like it should, sometimes not.

Hi,
I would guess that maybe you have felt it "skip" in gear. Sounds like worn out, chipped or otherwise damaged shift keys. The Deere part #M82826 is the key; it requires 2 or four depending on which of the three Peerless units your machine has. The transmission replacement Part #AM104533 replaces all three. Considering the age of the machine, I would first see if the rear wheels will come off the axles. They can often be difficult.
Should you have the tools and wherewithal to attempt the trans repair, the manual is here:
http://www.smallenginesuppliers.com/html/engine-specs/tecumseh/Tecumseh_Transaxle_Service_Information.pdf
And it is the 800 series unit.
Peace,
Clarke