[I've been leaning toward either the Lee Classic Turret Press,.... (If it can handle rifle reloading). Are any dies really better than others (costwise)?]
The Classic Turret is a good, solid turret press that every owner I've read about loves. It WILL do rifle stuff as well as handgun.
Lee dies are not normally my favorites but they actually do as good a job as any other and for a LOT less money. Get the carbide dies for handgun stuff and add the Factory Crimp Die for any excellant system for straight walled cases.
For rifles, I would prefer Lee's Delux rifle die sets (which includes a shell holder by the way, about $6-8 bucks additional with any other brand of dies). The Delux set includes Lee's excellant Collet Neck Sizing die as well as a standard Full Lenght sizoing die. Again, add a Factory Crimp Die and you will have perhaps the ideal rifle die set for getting started.
All I really don't care for about Lee's dies are the lock rings. They are easy for many folks to change the way they are set up. it's really not hard to reset them, nor does it take more than a few seconds, but it can be an irritant at tmes. Even so, don't avoid Lee dies based on the lock ring design. And some folks love that design, you may be one of them!
If you get some additional Lee turrets you may just want to load them and leave them ready to go. Turret heads would be about the same cost as Hornady's LnL inserts for a set up, maybe cheaper!