Then I'd build a giant safe, Scrooge McDuck style, and swim in my money.
Keep in mind, without constant connections, mobile, etc people are less likely to pop-in. It's a different environment, and thinking "What do they need" is different from "What do I have now, that they don't"
So if I could go back to 1995, I'd probably be working on that "User Friendly Windows Operating System" and maybe beat OSX out of the gate. Who knows how much success I'd have, but it would be a hell of a lot of fun. Besides, you said I'd have all the resources I needed to do it right!
EDIT: I just found out that Amazon was founded in 1994. I think I could still have a chance at rivaling Jeff Bezos though.
Actually I tried in 1995 but gave up due to:
(1) At the time, the Internet and/or dialup bandwidth was too small for sending pictures of people easily.
(2) I was trying to develop on OS/2, which seemed to be more advanced than Windows in 1995, but there the infrastructure for building such a Web site was still very poor.
(3) For storing photographs of people, hard disk prices were still too high.
(4) I was highly concerned about privacy, e.g., concerned that some pretty woman would have her picture and information on the site, and some wacko would download all that info, print it out, and put it up on trees, lamp posts, doors, walls, in men's rooms, etc.
(5) Believed that, still, really needed a walk-in local office, as was common at the time. That is, could not expect that could do it all with just a Web site. In the local office wanted an environment for couples to be introduced that would be safe for the woman.
(6) At the time, the matchmaking industry was moving from data on paper in books to video clips in VCR cassettes to be viewed in a walk-in local office. I wanted to have the video clips in digital form that could be viewed on computers in the office, but then the conversion of video from analog to video took way too much computing power, and the disk space cost was way too high. Also the operating systems didn't supply easy means of working with digital video.
(7) Was concerned about how to keep up the image and reputation of the company that it was for serious romantic matchmaking, e.g., looking for a spouse, and not for another version of pimps and prostitutes.
So, I gave it up.
Lesson 1: A lot of those 'social' concerns in the end people don't much care about.
Lesson 2: The infrastructure was not ready, and developing it just for that project would have been way too expensive. E.g., Firewire was just getting started; there was a prototype card for a few thousand dollars; there was no device driver software.
But all the infrastructure did become ready, solid, and very cheap but for much more general purposes than just romantic matchmaking. So, even if the needed general infrastructure is possible, likely can't afford to develop it just for one, narrow purpose but likely can get it for free if just wait until it gets developed for larger considerations.
Lesson 3: The project just needed to wait 5-10 years.