FCO is surprisingly reasonable airport. If you have US or UK passport you are eligible for automatic passport control on both arrival and departure, last week both took less than 1 minute - just scan and go no waiting.

There are 3 passport queues and it can be confusing which line is where , especially on arrival to T3:

1) EU
2) US, UK, Australia and few others - auto gates
3) All other passports

Do not make mistake to get into line 3 “other passport”, which can be very long. Surprisingly EU line was longer than number 2 on both arrival and departure, but not too long, maybe 10-15 minute wait.

edited to add: Any reason you prefer flying to Venice on a separate ticket vs train? Train will take
approximately 4 hours 45 minutes with one connection in Roma Termini. The advantage of the train is that you will arrive right in the center of Venice with many hotels and attractions with 10 minute walk. If you arrive
to VCE you need to water taxi or combination or bus / train which adds time and hassle — and you already have long connection in FCO and you will need to recheck bags with ITA and worry about missed connection etc.

If I could have single ticket and bags checked through, I would fly. Otherwise I would take a train and enjoy the scenery and more relaxed trip vs flying on separate tickets with long connection.