When someone comes to visit me at my villa, I would like to greet them and welcome them in. I know how to welcome English ("welcome"), German ("wilkommen"), and French ("bienvenue") guests in a single word. But if a native Roman comes to visit me, what should I say to him?
Pekkanen's dictionary suggests salve advenis/advenitis or bene adveneris/adveneritis, but I found no classical attestations of these. These are understandable phrases, but I don't know how canonical they are.
I dug around and found some relevant phrases in the literature that you might want to build on:
Plautus, Trinummus, 1097: et salve et salvom te advenisse gaudeo
Pacuvius, Tragoediae, 232: expectata advenis: salue, hospita!
Plautus, Bacchides, 101 (accepting a welcome, but can be turned around for a welcoming idiom): Bene me accipies advenientem, mea soror.
Cicero, De republica, 1.18 (on how someone was happy to welcome someone): eorum adventus periucundus et pergratus fuisset
Cicero, Epistulae ad Atticum, 4.19.1 (on arrival of a letter, but works also for arrival of a person): O exspectatas mihi tuas litteras! O gratum adventum!
It seems that if you want a simple everyday "welcome", then salve(te) is a good choice. If you want more flavor, use or adapt any of the quotes above.