Airlines from Barcelona to Rome

You're talking about a less than 2 hour direct flight - I would choose by price and convenience unless you're decidedly against a certain carrier. First, Google "Barcelona to Rome flights" to get the listing of airlines. Then check them out on Skytrax if you think the research is worthwhile. Skytrax has reviews and airline ratings (from 1 star to 5 star). I personally take reviews with a grain of salt (no airline is spared complaints, except maybe the truly exceptional carriers).

http://www.airlinequality.com/ratings/rating-background/

All airlines suffer delays.. and lose bags..

in Europe we have used Easyjet, Vueling, Tuifly, Aer Agean, and Ryanair.. multiple times.. they are all fine.. but you do have to read luggage limits etc..

Just choose cheapest.. I would look at Vueling and Easyjet first.

As for "service" .. er not sure what you mean.. inflight.. forget it.. all these flights are short.. you get a drink , you may , or may not have to pay for it.. but that's about it.. these are short flights.. most are less than 4 hours.. many are only an hour or so.. like a bus ride really.

Iberia and Alitalia are not rated so highly amongst the 'legacy' carriers, so I would also look at Vueling and Easyjet first.