I have used some form of oil, but have switched to a grease - whether you get something "gun specific" (and typically more money) like Shooter's Choice, or you go to the auto parts store and get a can of never seize, the results are the same - you want to easily remove the chokes, but not have it so easy they start to back out on their own - when shooting clays, hand tighten between stations often until you are certain they aren't starting to back out.
If they do start and do not check them, bad Ju-Ju can happen, up to and including injury and blown out barrels.
Depending on your clay game, an open choke, a middle range choke. and a distance choke will cover everything
Open chokes include Cylinder, Skeet, Improved Cylinder
Moderate chokes start with Improved Cylinder, then Light Modified and Modified
Distance chokes include Modified, Improved Modified, and the various types of Full
Skeet is typically shot with a skeet choke (.005)
16 yard trap singles can use anything from IC (.010), LM (.015), to M (.020), although most opt for Modified
27 yard handicap folks seem to like Improved Modified (.025) and Full(.030)
Sporting clays and 5-stand folks tend to utilize a wide variety of constrictions, but many of us tend to stick with those in the IC, LM, M, IM range. Since you get pairs at every station, the ability to utilize two different chokes to help in breaking targets set by folks with malice aforethought in their hearts is generally beneficial.....
The constrictions on Full can range from .030 to .040 depending on maker and bore diameter
As to steel - typically MUCH more expensive than lead, so unless where you live mandates it, don't bother.
Before buying any new chokes, try whatever came with gun - if they pattern well and shoot to POI/POA successfully, use them. If there is a constriction you want to add, they are available from a variety of makers