Make sure the Vet tests for both FIV and FELV and keep him in another room from your established cat until you know the results. FELV is VERY contagious.
When I bring home a new cat, I always keep them in the bathroom with a litterbox (tile floor, easy cleanup) until he makes at least one deposit of each. That way his smell is in that box and no matter where it’s placed afterwards he’ll regard it as his territory.
Of course I also have a food and water dish at the opposite end and a blanket or a towel for him to nest.
I find that being in a small space like that initially keeps them from feeling overwhelmed and gives them a feeling of security and let’s them calm down and settle in before they feel the need to explore the entire house.
And if the cat is the timid sort, at least you won’t have to go around fishing them out from under the bed or whichever other inaccessible area they choose to hide.
You can spend a little one on one time with him in there and get acquainted.