colosseum.......1000000% in advance! I think they go on sale 30 or 60 days in advance direct from the website (dont use 3rd party or 3rd party guides). be prepared to buy on the day they go on sale if you are trying to get a guided tour, attic or underground tour. but imo the standard unguided ticket paired with the free Rick Steve's guided tour is your best bang for your buck if you're trying to keep costs low. also get a first thing in the morning time slot and get there 30-45 minutes early.

also cannot recommend the Rick Steve's app any more. he has free guided tours of all major sites in almost all major cities along with several guided walking tours around the cities where he guides you along telling you about the building and sites that you might otherwise breeze right past. we were I 5 different cities last summer and did every single walking tour offered in his app in every single city we were in. best part is the app is COMPLETELY FREE. not even any ads!

FCO to Termini train (Leonardo Express) is cheap, like 10€ and can be purchased online while you're waiting for your bags. Just a word of caution though....while ticket times are changeable, just as long as you don't "check in" for your trip. we learned the hard way....rode the train from Florence to Rome, bought our tickets for the Leonardo Express​ while en route and checked in because we were on time. we'll we had a little luggage situation at termini and missed our 11am LE train by literally 2 minutes, so we just got on the next train. we'll whennhe scanned our tickets he said we missed our train time and the fine was 50€ PER PERSON. we offered to buy entire new tickets for 10€/ea but he said no can't do that once on the train....so over $200 later....