Italy with a first timer as a young couple on a budget

I strongly suggest you purchase Rick's book to begin your research.
It's super useful for beginners and veterans in traveling.

When in Vernazza be sure to travel to Manarola to eat at least one meal at Dai Billy. You will not regret it. And go to Miky in Monterosso. Try the anchovies.

Thank you very much for the advice! I do have the book and have been studying up, just looking for more targeted recommendations (since there are a good many in the book) and also some more unique ideas for tours!

hey hey amiller131
welcome aboard. is this trip in 2 months? if so you are late getting started. how many nights do you have, without adding your arrival and departure days.
it will probably be HOT, very crowded, during high high season (summer), jubilee 2025 the holy pilgrimage in rome expecting millions
from all over the world. after rome many will want to go to the same places you want to see. have no idea what your budget is, many places have been booked since last year and slim pickens with higher prices
booking.com/trivago.com/tripadvisor.com would be some accomodations to check out and see what's available for your days or do you have hotels booked already? italy is not a budget place like it use to be unless you stay out in a small village in the country but then transportation is something to think about. remember check-in to hotels is 2-4pm and check-out is 10-11am.
trenitalia.com or italotreno.com are the train companies in italy, make sure you use italian names for stations
besides, trains, planes and automobiles you have the onslaught of summertime cruise ships adding thousand of passengers, especially the cinque terre (notice spelling) and taking trains to florence. been there done that and it's CRAZY, packed trains and if full breezing right by stops/stations, italian time is just like hawaiian time "slow and relax"
i don't really recommend restaurants, walked down the small alleyways/calles to small mom & pop family owned places away from tourist central with waiters hanging outside holding menus. prices have gone way up on tours/activities/dining like everywhere else. happy travels & enjoy
aloha

It is not clear to me how many nights you have for this trip and how you are allocating them to each location.

Knowing how long you will be in a place makes it easier to suggest what the 'don't miss' list should look like.

I appreciate all of the advice! For clarification:
1. I have already booked our accommodations
2. We will be staying in Florence June 25th-28th (3 nights), we will train/bus to Siena on the 28th and stay one night (June 29th), then we will train to Vernazza and stay 3 nights (June 29th-July 2nd), then we will train to Milan and stay the night before flying out early on July 3rd.

I'm going to throw out that you are adding a lot of travel time for one night in Siena. I know you have your accommodation booked, but I would personally try to add a second night to Siena. Or one night in Lucca ,for example ,is more on the way to the Cinque Terre if you can find the right train connections.
Re whether to book ahead for trains, I have not in Italy, other than once out of the Cinque Terre to Rome the day before as it was filling up. However we travel in shoulder season, April/ October so I hope someone can weigh in with better information. I like the flexibility of deciding what time I want to leave
In terms of budget. All of your places are more touristy, so meals will be pricier. Siena was the most reasonable of them in my experience last time, which is another reason for my suggestion to add a day there. In the Cinque Terre you might need to reserve beforehand, ( certainly for Billy's)

hey hey amiller131
so happy you got your accomodations reserved, that a great accomplishment. more people will give you lots of info in cinque terre.
you days are short but gives you time to see and do things, get out early before the crowds then late afternoon/evening after crowds leave and hopefully restaurants are less busier.
florence: what ever main attraction you hope to see may need reservations, some are date/timed stamped
educated-traveler.com/ wine windows of florence.
lots of history here, as door windows and what was used for. stop at a window and order a glass of wine/pastry
eatingeurope.com/ florence
a few tours but dinner tour with truffles, florentine steak & fine wines is a special with 30% off. top of page and book by april 1st
also a pasta making class at local's home, right up your alley in post, plus tuscan wine and my favorite tiramisu
paintandwineflorence,it
paint a picture souvenir to take home along with wine
mercatocentrale.com
local fabulous market, click artisans, enjoy roaming around stopping in shops and having wine and appetizers.
florencetown.com
boat (gondola) tour down the arno river
stopped for gelato, picked cone & flavor, took picture of cone in front of name of shop, it was our mission to pick best place
florence station name is santa maria novella
stop at the many patisserias (bakery) for all the yummy goodies or "deli" for sandwiches and other foods sitting outside table to people watch.
cinque terre:
cinqueterre-travel.com
lots of things to see and do. click tours & sea. swim with the mermaids, something fun and unusual.
click other villages and what they offer, some wine tours for you. many areas all over italy have vineyards not only tuscany, which are more costly. stay near your place instead of many hours away.
nessundormacinqueterre.com
learn how to make pesto, click the wine experience, cantina marinella for wine tasting in manarola. take the train to other villages early morning ahead of crowds and roam around. stop at outside table to have wine and appetizers/homemade focaccia and people watch. another thing to check out is:
cruisemapper.com
click port and either la spezia or livorno, the days you're in cinque terre, click june and july 2025 shows you how many ships are in ports, scroll down to ship and see how people are on board to get off, if 4 ships could be 15 to 20,000 cruisers. go the other way up the coast. i've been one of those cruisers and many can be grumpy and pushy, we just stay in the towns/villages. roam around the shopds, bring you swim suit if you want to swim at few of the beaches (even water shoes "tabis") not all beaches are sandy.
when ready to take train to milano centrale pick up a bite to eat before boarding, bottle of wine, make sure you have a corkscrew and enjoy a "train picnic" and enjoy the views and ride.
give yourself 3 hours check-in time to milano airport (MXP) for immigration/passport and one hour getting to airport. we alwyas buy food at airport for our long flight home where ever you are flying to. when in milan eat risotto which is the home of "rice patties"
these are my own thought and opinions, seen enough art, museums, churches, statues and want the fun away from them
enjoy your time and breathe the italian air. you can't see it all. you'll probably be planning your next trip on your flight home. always come back for any questions and info you need and hope for, posters here to help you.
aloha