Just about any grease will do I think, but I'd stick with Shimano grease. For oil, I prefer rocket fuel.
Less is more when it comes to grease and small precision moving parts such as in our reels these days:
"The application of grease is important. Grease should be applied at the base of the gear teeth so when the teeth of the gears mesh together, the grease is being used as intended. Wiping the outside of gears with grease will cause the grease to splatter inside of the reel and all is lost. Grease with a good temperature rating is preferred. Never use Vaseline."
"Rocket Fuel oil is available in three viscosities. The Tournament is very thin and used mostly by anglers in Casting Contests and must be applied quite frequently. Next , is the Yellow and is of medium viscosity and is used by most of us anglers. It doesn't have to be applied as often, Probably twice a season , depending on how much reel is used. The last oil is the Red and is the thickest and used by anglers wanting to slow down their reel. Rocket Fuel possesses slightly adhesive qualities at the start of the cast, yet is free running at end of cast. It will not evaporate, so the reel bearings will not film over, or have the oil in them turn to sludge. The oil will not mix with water, has a wide temperature range. It is not affected by any normal temperature differences and due to its slightly adhesive qualities, it will not easily be thrown off."
http://www.lakeforktacklerepair.com/techniques.htm