Although I do have a tapered prop reamer I use the stepped type with the straight shanks. I do not use prop adapters or savers so my props are going onto a straight machined crank shaft and have a slightly snug fit completely through the hole. That's just how I do it and the prop reamers can be found in most hobby shops or ordered through tower. I know people that have knocked out the Tee handle and chucked them up into a drill press for quicker/easier reaming. I do think the stepped reamers are a much better tool for people new in the hobby.
Ground clearance of the prop? A trainer is going to take some hard landings so I would go with the smaller prop. Some of my own planes have less then 1/2 inch clearance but I know how to land them without a prop strike but I have gotten chips taken out of a prop from hitting small rocks on take off more then once.