Trenitalia (official train company) has direct fast trains to Salerno 11, 12, 1 it is a 2h 6m journey
Also has direct IC trains at 11:26, 12:26- journey is 2h 58m- IC trains are similar to fast trains with reserved seats- just makes more stops
(Direct does not mean Non Stop)
https://www.trenitalia.com/en.html
ItaloTreno (private train company) has direct fast trains at 10:40 and 1:40- 2h 12 m journey
https://www.italotreno.com/en
Download the apps for both, set up your accounts and familiarize yourself with it
Once you are through Immigration/EES and have your baggage you can use the app to book your tickets. Or you can purchase at a kiosk or window at the station in the airport.
Search for
Fiumicino Aeroporto to Salerno
That will include your Leonardo Express leg. You will want maybe 30 min maximum between that and the fast train from Roma Termini. If you need to grab a bite give yourself more time. I suppose you could book each leg separately if you must
The Leonardo Express runs every 15 min- no reserved seats- 32 min journey to Termini
I'd guess you could be on the 12 or 12:26 Trenitalia train- it is possible you could make the 11:26 but I would not expect any earlier than that.
Wait til you get there or buy REFUNDABLE/EXCHANGEABLE tickets. You will have to read the restrictions and rules and know what to do to change your ticket. (Honestly I would not want to deal with that on a jet lag arrival day)
Just buy tickets when you get there. There are plenty of seats available- Base Rate is 53euros- which is what you would end up paying if you purchased a discounted ticket now that you end up not being able to use.