Airport trains run 365 days a year, even during strikes. So if you are staying close to Termini station and you are leaving from FCO, you have nothing to worry about: pay 14 € and get on the Leonardo Express .
The FL1 train to FCO that serves only secondary stations like Tiburtina and Trastevere will make only a few runs on April 25, you'd better check while you're there.
If you are departing from Ciampino you'll have to take either a cab (there is an "all included" fixed fare from central Rome) or a bus, but bear in mind that buses will run on the reduced Sunday schedule.
I can't see a single reason to waste money on a private transfer, but of course do what makes you travel in a better mood.