Records not stored vertically for decades

@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!  

@soix 

As to the integrity of the grooves storing them horizontally, if the vinyl is stored in paper sleeves, paper deposits will probably be encrusted into them deeper, hence you'll need some good wash. I use ultrasonic. And then switch to plastic sleeves. Other than the covers at the bottom probably suffering some visual damage, you should be fine but it will take work. Vinyl requires a lot of time to get started but once the equipment is properly setup and the records cleaned and stored in plastic sleeves, you're good to go. Also use plastic sleeves to protect the covers. A tip of mine that no one ever mentions: SLIDE THE COVERS OPENINGS IN FIRST. That way dust will never enter the covers. Simple but totally effective. And store them vertically.

You should buy a quality disc washer 

For $2-3k you should be able to get one that washes

Dries. Myself csnt be bothered with high quality digital being so good 

But disc have their own qualities my brother disc washer 

Is to me expensive over $5 k  check with

The needle doctor or others  on quality, pricing.

What fun you will have re-discovering those recordings.

Checking if flat on glass is a good idea. If not flat, a Shure cartridge with a damped brush would be a good idea.

My favorite elliptical with damped brush is M97xe

M97xe, good price

Other aftermarket stylus replacements that have brushes are not damped, like my Jico replacement for my Shure V15Vxmr. Great stylus, the brush is good, but not as good for warps as damped. 

btw, you can play these cartridges with the brush down/working or up, they simply click in up position.

My other thought is that some paper dust might be pressed in the grooves more aggressively than vertical, i.e. not easily dislodged.

My old LP's sound significantly better after a good manual scrub. I do batches of 10 at a time, the brush is a baby scalp brush from Amazon

baby scalp brush

I've had records that were stored flat for months to years and never had an issues with them.  I think as long as they weren't submitted to excessive heat or humidity they'll be fine.