Either way, TAs are a wonderful way to go to or come home from Europe. We do at least one and usually two a year, and for us, the coming home choice works better. Nothing beats floating home for a leisurely two weeks after walking miles on vacation. The gradual time-zone a day adjustment allows you to arrive home un-jet-lagged. Going outbound, we found that the first week or so is nice, but a port a day for the last 4 or 5 days with time changes was tough and got us there more tired that we would have been flying.
As others have mentioned, the westbound TAs leave in October, and a few as late as November. Keep in mind that the ships, except some of the Cunard ships, are finishing up their summer seasons in Europe, so are squeezing every week out of the fall season before taking off for the US and eventually the Caribbean. Cunard's TA's run year-round between New York and Southampton, but only take a week. Southampton is a bit of a slog to London, but manageable by transfer (e.g. bus). We haven't tried to get there other than using the cruise transfer so I don't know what other transfer means are available.
Cruise lines often offer much-reduced airfares to Europe if you're picking up the ship for a westbound TA. Last year, we each paid $150 one-way on Lufthansa from Washington DC to Nice. Same thing for previous sailings from Rome and Barcelona. They don't care when you go over. Last year we were in France for a month before making our way to Barcelona for the trip home.
Much like travelers, cruise lines vary greatly. They have 'personalities', so do the research to find a line that fits best with you. Over the years, I've been on Carnival (Pretty much a floating frat party, but that was 10 years ago; maybe they've changed.), Norwegian (a little more sedate), NCL (similar to Carnival but with an older crowd), Royal Caribbean (big ships for the middle-aged demographic, we found), Celebrity (a more 'mature' demographic who enjoy a quiet experience with good food and varied entertainment. Their Aqua Class provides exclusive access to a great spa and restaurant.), and Azamara (considered to be a premium line, but, as the ships are considerably smaller (600-700) people, there more limited choices for entertainment and a smaller spa.) Smaller, more upscale lines with smaller ships like Silversea and Viking also make the crossing.
As mentioned, CruiseCritic is a goldmine for ship reviews, deck plans, social events, and other information. We've used the roll-call tool for joining other passengers and splitting the cost of private tours.
Itineraries are often very similar. For the lines above, you generally leave from either Rome or Barcelona; a few leave from Southampton. There may be others; depends on where the line is finishing up the Europe summer season. Civitavecchia, Rome's port, is a good hour away from Rome itself, but cruise lines offer bus transfers and there is public transportation as well. Many people just stay in Civitavecchia to avoid the commute from Rome. Barcelona's is very close to town. The Azores, Madeira, Gibraltar, the Canaries and Hamilton are frequent ports of call.
I'd strongly encourage you to arrive at least the day before your departure, east or westbound. It's worth a night in a hotel for the peace of mind. There are "cruise hotels" from which the lines run transfers. If you're staying the night before, look around. Prices at cruise hotels aren't necessarily the best. booking.com might have a better rate for the same room, for example.
As for choosing a stateroom, coming back across the Atlantic in late October, you don't have a lot of time to enjoy a balcony - too cold, although those cabins are brighter. Interior cabins are much cheaper and a good buy if you spend little time there. They are dark and smaller though. If you like the pool, verify the ship has a covered one. Some don't. Lots to think about....