The 1894-S Barber dime is proof only, so it would not be included in a full set of circulation strikes. The Barbers would be easier to complete as a full set, but the Mercs are not out of range if you get the 1916-D in AG grade. But the 1921 is also a hard date. Another option is to complete a short set of Mercs, or a date set only, where you just get the date and it's your choice as to the mint.
I do wish to remind the OP to collect whatever floats your boat. Don't let the "But Barber Dimes are really hard to collect" train of thought detour/discourage you if you really like them more than Mercury Dimes (hard to concieve, I know, but possible I guess). Just may take you a tad longer for the Barber series, but always collect what you are more interested in. Ok, off my soap box.
I'm working on and off on a date set of morgans, it's the only way I can afford to do it, haha. The two worn examples of 1894-S dimes certified by NGC aren't grades as proofs, merely as G4 and AG3.
Why are people doing prices for MS? I'm pretty sure he's just going to a nice cirluated set of Mercuries or Barbers.
I agree the best advice is collect what you like the best. I like both Barbers and Mercs, but I am completing a complete Liberty nickel series, mostly f-VF, but the 1885 I have to get in Good. I'm also completing a date run of Barber halves. I guess I like a lot of series, but Barber designs are very Roman like and maybe that's why I like them. You can get common Barber dimes in VF for a song, complete with full Liberty on the headband.