I run a 10-speed Tiagra short-cage with a 12-28 cassette. With your long-cage derailleur you can run any cassette Shimano makes. Which you choose depends on terrain. Changing a cassette takes about three minutes and the tools cost about $20 .... less than half that if you make your own chain whip (as in, just use an old chain.)

I run a 50-34 crank set and with 12-28 I can make it up most hills but I live in Flatahoma, where "long, steep hills" are a quarter mile at 5 percent---and rare.

Mathematically, as [MENTION=385973]mstateglfr[/MENTION] notes, you can handle a max of 32 teeth, but ignore that. Your RD can handle the 11-34. His math is correct---not disputing that--but as he notes, "Shimano is conservative with their published max numbers for cassette cog max."

Seriously, with that triple, 12-28 ought to work for everything except mountain-climbing .... unless you are fat, old, and weak like me, in which case you can fall back on the 11x34.

Whichever cassette suits whichever ride, you have all the gearing you should ever need.