First, any video transfer business will not transfer copyrighted movies, which you say is what you have. So to transfer those movies you'll have to do it yourself.
Movies on VHS have copy-guard, when you hit record on the other machine the screen will start flashing, making it unbearable to watch. You'll need a filter that can eliminate the copy-guard. This video will show you how to do that, here's a link.
How To Copy VHS Movie Tapes When You Can't in 1986 - YouTube
If it were me, I would buy a cheap VCR at a pawn shop, Goodwill, yard sale, but I wouldn't spend anymore money than that. The best is to just give them away, and go to Walmart and buy the movies you like on DVD in the $5 bin. They'll last forever, the VHS tapes I'm surprised they lasted this long.