I would first replace the tyres and see what else needs to be addressed after that. I would suggest something like the Specialized Turbo Pro or Specialized Fatboy if you want a little more cushion. If your streets are a bit rough on tyres, you may want to go with something like the Specialized Nimbus Armadillo plus maybe some Mr Tuffy liners for extra added protection. If you want to go cheap, Specialized has the Tri-Sport. I just converted my wife's hardtail to some generic Pyramid slicks in 26x1.25 for pretty cheap. They're ripoffs of the IRC Metro... same tyres made in the same factory... just different label and lower cost.
Also, does the bike have a suspension fork on it? If it does, then you might find it advantageous to swap it out for a rigid steel fork such as the ones from Surly (1x1) or Kona (Project 2). Make sure you get a fork that's suspension-corrected. They should cost somewhere around $50. Suspension on pavement generally wastes a lot of energy and is really unnecessary.
Other things you'll probably want to invest in are of course a helmet, emergency kit that includes a spare tube, patchkit, minipump and minitool. Make sure you know how to use them. If you'll be commuting or riding at night, you will probably also want lights. You'll definately want a rear blinker or possibly even many blinkers and depending on your riding conditions, a cheap LED front light may do the trick but for darker conditions without the aide of streetlamps, you'll likely have to invest in a high quality lighting system. These can get pretty expensive. Maybe look for used ones. There are a few other things you may want such as a rack if you intend to carry stuff. Do a BikeForums search for things like clothing and accessories.
As far as comparing it to current bikes, it depends on what's on the bike. How old is it? I distinctly remember the Trek 850 in the early 1990s as being the top-end recreational steel line of MTBs with the 900-series being the racing steel line of MTBs. It was made with Tange double-butted cromoly with a cromoly fork and mid-level components. Trek used TruTemper AT steel for their 900-series. That 850 is a nice find as there aren't too many steel MTBs still being made. They generally filled the same market position as today's Trek 4500 and 4900.