Some pieces of advice based on common issues with 1st generation (87-90) Legends:
As long as you're changing the battery, you might as well get the alternator tested. They tend to go bad on our cars, because they're insufficient to power the car's infinite accessories when idling or during slow city driving, which means they're under full load recharging the battery once the car gets on the freeway. There's a thread on here somewhere about this, and about how Acura actually made a change to the alternator pulley size, along with part number information for the new pulley. Couple that with the thread about Acura of Agusta's recession pricing, and you've got yourself a (relatively) cheap DIY!
That rear window could probably be fixed with some Honda window motor grease, unless the motor itself is burned up. Like $12 from AofA.
keep an eye on fluids, depending on how many years it's been I would just change everything you can right now. Make sure you use Honda fluid for the transmission.
I believe Prestone or Peak coolant works in the Gen1's, but if you really want to, a lot of people on here would recommend Honda coolant. But it is a bit more expensive. The only difference I know of is that it's blue rather than green.
Make SURE the timing belt gets changed by the time you hit 180,000, and you'll be good to go.
Our cars have similar histories. The original owner had a ton of money and kept it in like-new condition. He hit an object in the road around 30,000 miles, and had to have a large portion of the equipment on the back right wheel/axle/etc. replaced. Not sure if it hurt the frame or not. Other than that, he did all the regular maintanance, even got the alignment checked every 10,000 miles or so. As near as I can tell, the car has NEVER been out of alignment (except for my recent camber problems, most likely just due to old bushings, I don't think the control arms have ever been replaced). After he was thru with it, at about 140,000 miles, he sold it to my dad. After two years of ownership, my stepmom got hit by some random guy at a stoplight, and the insurance SEVERELY underestimated the market value to be $1700, so they could total it. All it needed was a new front right fender, no internal damage whatsoever, but the fender repairs cost $1400. My parents put maybe 7,000 miles on it, then, because it needed a salvage title due to being totalled, it sat in my parents' garage for two years once the registration expired.
Until September, when he gave it to me for free. Unfortunately, my dad didn't take quite as good care of it as the original owner, as these days it leaks oil a bit (although it's really not economical to seal the leaks at this point), and the automatic transmission fluid is dirty. Thus, when I get some money and a free weekend, I plan on draining and filling it like 4 times to clean it out. On the ATF versions of our car, the pan holds like, 1/3 of all the ATF in the system, so if the fluid gets dirty, it's an ordeal to replace anywhere close to 100% of the fluid to clean it out.
But the car is REALLY clean, and in GREAT shape. You can find pics in this thread:
Finally got pics of my car