Should I make my train reservation a month in advance?

Absolutely, and you'll save money. You should start looking two months ahead when they go on sale.

IF you want to take advantage of the discounts available AND lock yourself into a fixed schedule, then the earlier you make a reservation the better. At a month out, you may miss some of the better discounts. Discounts are limited to specific trains and times so it is possible that all the discounts will be sold out a month in advance. If that is the case, then it makes no difference if you purchase an hour before or a month before.

When you ask, if it is OK, I am not sure what you are asking.

You can purchase Trenitalia tickets up to 120 days in advance, but December and June schedules (when schedules change) probably won't be available that far ahead.

You can buy them online and you will get a print-at-home ticket right away via email.

Actually Zoe, I was surprised myself (a veteran purchaser of Trenitalia tix) to find December -and-beyond schedules released ahead of the normal schedule change. They were not 120 days out, but they were more than 90 days out. I actually missed the lowest fares because I thought they would not release last Dec fares until 15 days before the schedule change planned for (I think) Dec 8. I got lucky because I checked about 100 days out. So watch watch watch those fares starting 120 days out, no matter the time of year. As soon as you are sure of your dates, make the reservations.

Also, Italo tends to allow booking pretty far out. They are a worthy alternative.

Laurel, you are right, I start checking 120 days out and the new schedule can be posted anytime, but there's usually a less-than-120 day window.