Yes certainly he needs to be neutered asap if only to reduce the likelihood of him spraying. If he is initially very nervous, you may want to set up a place of safety for him. Somewhere to hide away so he can feel safe. A cardboard box would do it and then just sit on the floor/lie on the bed in same room with a radio on low. I always sleep overnight in same room with newbies for at least a week but then I'm a crazy cat lady
As regards your partner bonding, play is always helpful with this as is food. There are some fabulous toys in the Purrs Shop.
As he is more recently used to being outdoors, I would guess he may start whining at the windows/doors to get out pretty quickly. You will need stand firm for at least a few weeks so that he learns where his new home is.
Hoping all goes well
to Purrs by the way. Hope you stay and let us see pics of your new lad