Some basics first. You will want to fly "open jaws," into one city (say London) and out of another (say Rome). To find these flights, don't look at two one-ways, but at the "multi city" option on booking sites. Even if it seems "more expensive" than flying round trip (and it isn't always) you save time and money by not backtracking.
As for which destinations or routes are cheaper: there is almost no rhyme or reason in flight prices any more. So, you'll just have to check yourself. You can use Kayak http://www.kayak.com/flights or Matrix ITA http://matrix.itasoftware.com/ to do this. Matrix ITA allows you to check more than one place at a time. For instance, if you put "LON, PAR" in the destination box (without the quotes), it will search all London airports and all Paris airports.
I don't know if Air Transat shows up in those search sites; if not, search it separately.
As for where to go, that's up to you. Once you figure out your four destinations, how to get between them will be easier to figure out. For instance, if you were only going to the three you listed, I'd say fly into London, take Eurostar train to Paris, fly to Rome, and fly home. If you do it in reverse, you may get better weather, but will probably pay more (London airports have high exit fees that are built into the ticket, so it costs much more to fly out of London than to fly in).
Unless you have a special interest, Milan is not usually found to be as worthwhile as Venice or Florence. Barcelona is not particularly easy to get to from your three destinations; there is now a fast train from Paris taking about 6 hours, but you'd have to fly to Rome or London. Of course, if that's where you want to go, that's what you should do. If you want a big city in a different country, consider Amsterdam or Berlin (both different from the three you are visiting, with lots to see and do). Or go further east to Budapest or Prague or Vienna (each of those three is VERY different from the other two, by the way, despite the fact that they're often mentioned as triplets, like I just did).
I'd start by reading travel guides and looking at videos, to see what interests you.
As for overnight trains, opinion here is very divided. While Rick (and some others) remain fans, others say "never again." If you don't sleep well on them (and you won't know until you've tried it), you arrive tired, unwashed, and cranky.
To research flights within Europe, use Skyscanner http://www.skyscanner.com/. To look at train schedules, use the Bahn (German rail) website, following Rick's tutorial: http://www.ricksteves.com/plan/tips/db_tips.htm. For LOTS more information about trains, look at The Man In Seat 61: http://www.seat61.com/