The only thing you need to do is ensure the bike is safe to ride. Do a methodical M-Check on the bike, look over the whole thing and ensure nothing's deteriorated.
Your rim brakes will be perfectly adequate at braking - sure they may not be trendy but they can stop you fine. There is a possibility that the pads have hardened with age and need replacing, But they're consumables, so two pairs of brake pads are cheap. Just get Kool-Stop ones.
Also look closely at your tyres/tires. If they have hardened and cracked and dropping rubber then its time to replace them. You could choose some small-knobs or tyres with no knobs. But if your current tyres are okay then just ride them for a couple months. Your tubes may be okay, or possibly not. Try inflating them to pressure and see if they hold air pressure for a couple days without loosing more than a few PSI. Again tyres and tubes are consumables so replacing is just normal usage. If you do change to narrower tyres, you'll need narrower tubes anyway.
If your bike has a suspension fork then that's probably the biggest unknown. If it works fine, then keep using it as is. Riding around on a failed/frozen fork is workable but is additional weight and there's a chance it may move unexpectedly on you. Replacing a fork is probably too expensive, unless you have a suitable donor bike of similar specs. Riding on the road does not need suspension - you don't ride into kerbs/curbs or potholes. Normally the suspension would squish if you push down on the handlebars and rebound to the initial position.
Give it a year or so of riding and then you'll be in a better position to know what you want from your bike. At that time, you might choose to go for a dedicated road bike, or simply keep pedalling your current bike.
You can own more than one bike, that's totally fine. (I have 5 1/2)
Faded paint, ripped saddle, or similar are mostly cosmetic - either patch them as you see fit, or put up with it. Even light surface rust is generally not a problem as long as the bike works and remains safe to ride.