Same car here, had it for the past couple years. '07 V8 Sport. Bought it with 95,000 miles, now at 119,000 miles. There are def things to look out for, but it has been a reliable and comfy roadtrip/camping/wife&kid car. No balance shaft issues, knock on wood. Note, this is for a dealer -maintained 1-owner example, although dealer-maintained doesn't appear to mean much (records show basic maintenance was all they did - oil, brakes, routine maint interval checks):
1. Trans, valve body pre-2008 - had some slipping issues initially 2 years ago. Replaced the fluid, it has been OK since (the old fluid looked like orig - nasty)
2. Accessory belt, idler pulleys replaced - 2 idler bearings died, sounded like an Aerostar when they were new, belt was cracked, was original
3. Engine mounts - replaced passenger side, and trans side
4. Struts/shocks/front LCA bushings/strut mounts replaced
5. HID bulbs replaced - due to intermittent flicker
6. Alternator replaced - was original, started dying early 2018, known to last up to 10 years (usually less due to heat), replaced with Bosch reman, bit of a pain to do due to space constraints. I hope to never do this again
7. Battery replaced - orig, old, dying alternator didn't help
8. Spark plugs replaced - routine maintenance
9. Bought Volvo VIDA - to help with maintenance
Could've been worse - just stay ahead of the potential used car issues as much as possible. But I love my '87 even more now.
Find a 2008+ if you can, and you avoid both the balance shaft and trans issues.