Flying into Rome how much time to allow to get through customs?

Three hours should be way more than enough. Customs in Rome is pretty perfunctory; I don't think we've ever even had to slow down. If you check bags, you may have to pick them up before your transfer, but it still shouldn't take long. Moving from one terminal to another will also take a little time; when you book your Venice flight, see what terminal it leaves from.

If you are not flying with one ticket, and you are taking a low cost airline to VCE, you need to retrieve your luggage and check in again at T1 (you will arrive at T3). The issue is more whether the flight arrives on time, which you can't know.
There is also the possibility of going by train, which is almost as fast once you factor in waiting time and transfer from Venice airport to the historical center of Venice in the middle of the lagoon. The train station is on on the Grand Canal.
There are 2 direct high speed trains that depart from the airport headed to Venice, at 11:08 and 15:08. At all other times you can take the Leonardo Express train from the airport to Roma Termini (32 min) then transfer to a high speed train to Venice Santa Lucia station. There is at least a train every hour from Rome to Venice. You can buy tickets at the airport station.
Check options on:
www.trenitalia.com
The departure station is
FIUMICINO AEROPORTO
The Arrival station is
VENEZIA SANTA LUCIA

Customs and immigrations (passport control) are two different issues. Customs is mostly a walk through the green door - Nothing to Declare. It will take 30 seconds and maybe a minute if there is a line. However, immigrations is a whole another issue. It can take 30 minutes to two hours or more depending on the number of planes arriving and the number of officers on duty. Last time through Rome for us was two and a half hours. Only two officers checking passports. Conventional wisdom is that you don't buy tickets for the onward journey for the day of arrival unless the tickets are refundable, buy insurance, or you can lose the cost of the tickets. After thirty years of travels and we thought we knew how to cover everything. We had some easyJet tickets flex tickets for a flight four hours after we arrived. The flex tickets would allows us to change to another flight if we missed the original flight. Our international flight was cancelled and our rescheduled flight two days later did not arrive at that airport so we could use the easyJet tickets. We lost the tickets about $150. So we will be more careful in the future.

Yes, I had forgotten about immigration. If Rome is your first stop in the EU, you will have to go through passport control. I don't think we've ever spent more than 10 or 15 minutes in line, but obviously, it could take much longer.

I do like the train idea, especially if your schedule allows you to take one of the trains directly from the airport.

Unless you are on one air ticket to Venice (for example with Delta/Alitalia), in which case you are covered because they would simply put you on the next Alitalia flight to VCE at no cost, I wouldn't chance it with a low cost airline with a separate ticket. Too many things can go wrong. In many occasions I arrived very late or even had to cancel till the next day.
I would go with the train, purchasing the ticket when I get to Rome on the spot. The one way train cost (full fare base price on 2nd class) is €88. Not sure if an airplane would be much cheaper, I doubt it, once you include the cost of the taxi from the VCE airport to the city.

I don't check bags and go carry-on only. My best time from plane to clear immigration and ready to head to Rome was 20 minutes. Helped I had a seat in the front of the plane and was one of the first in line and no others planes landed when we did so the line was nobody. But a couple of other times it was about an hour.

I've found Milan to be a little quicker with customs and cheaper on flights that I try to go into that airport for arrivals.

Thank you so much, this information was very helpful.

What we do is either book a single ticket or else buy train tickets on arrival at the FCO train station; they will sell you the ticket to Termini and then the ongoing fast train ticket to Florence or Venice which you can make. The tickets are more expensive last minute but in 10 flights to Europe in the last 10 years every one of our flights except one has been late on arrival from half an hour to 5 hours. The 5 hours was unusual but half an hour to an hour is common. We did arrive once in Rome half an hour early. If you buy plane tickets ahead be sure they are cheap and be prepared to lose them if things go awry. I would probably leave 4 hours since you will have to go back through security. You will almost certainly have time cooling your heels if you do this, but you won't be biting your nails if there are short delays at departure either.

Be sure they stamp your passport at Rome immigration. Last time we flew there they just waived people through without even looking at passports. When we went to leave from Amsterdam we were pulled out of line and had to prove our date of entry. I had Etickets, hotel bills etc and could document our trip; the guy who was pulled with us did not have this information and missed the plane. Americans have 90 days max in Schengen without special visas and some exit airports enforce the Schengen rules. This took an hour or so and they retroactively stamped our passports for entry before letting us make the plane and exit the country.

+1 vote for train, as Robert said. It takes about the same amount of time but you can see some of the country as you go along. Probably better/roomier seats, too.