@soix Here's my best guess as to what you may eventually encounter:
If the stacks were perfectly stacked one atop each other (i.e. records and/or jackets not askew here & there) so that there was equal pressure on each disk and the floor was perfectly flat, the top 5 to 7 records of each stack might have some degree warping. I don't think you have anything to worry about regarding groove damage. The major concern, I believe, would be dust, mold spores or other fine infiltrates in the storage environment, especially if the records were not ensconced in and inserted properly into good quality anti-static inner and/or outer record sleeves. If I were you, I would invest in a good record cleaning machine or system before playing those records on a good TT. Depending upon how much you want to spend, there are a number of record cleaning options to consider (e.g. ultrasonic, vacuum machines; manual cleaning; etc.). Have a read (i.e. not an easy read but worth the time) of this: Vinyl Record Manual Cleaning Process (thevinylpress.com)
Investing in a good TT is, obviously, also a must if you want good sound quality. If you ultimately decide to go ultrasonic cleaning and don't want to spend 4K or more on a nifty ultrasonic cleaning machine, have a look at this: CleanerVinyl Ultrasonic Record Cleaning
Good Luck!