When storing records it is important to ensure that the place you store them is cool and dry. Vinyl records do not react well to heat and will warp if left in direct sun for even a short period of time. I had a friend once that stored a number of records directly on a wooden floor that turned out to have damp issues and the rising damp caused the record covers to mould and in a few cases even caused the paper sleeves to stick to the vinyl itself. The general rule for me would be to only store records on good sturdy shelving, off the floor and away from any direct sunlight.
Also make sure that your records are placed vertically, and not stacked horizontally, to prevent having weight on them that can lead to warping or buckling. Vinyl weighs a lot more than you think!
There are many easy storage options available from most major furniture retailers, and also from Amazon.
I am of the opinion that the less is done to a vinyl record the better and some over enthusiastic methods of cleaning may in fact do more harm than good. For most of my records, once they are clean a simple brush down with a good quality anti static record cleaning brush before I play them is enough and is probably all they will need for most of their lives. I always lay the record down flat on the record player, start it up and while it is spinning I lightly brush any excess dust off like this:
Some people will object to this method because they say it wears out the turntables belt quicker, but honestly I never noticed any extra wear and to my mind belts should be replaced once a year anyway. Trying to do it while holding the record complicates the process and could lead to getting fingerprints on the record or the record being dropped, which is not a good thing.
Your turntables stylus is an extremely important part of your whole setup and can ruin your record collection if it is not taken care of properly. First, be sure to replace your stylus every year or two, depending on volume of use, with as good quality of stylus/cartridge as you can afford. A worn out stylus will damage your records! And second, be sure to dust off your stylus often to prevent dust build up that will dampen the stylus movement, leading to degraded sound quality. NB: Be sure to use a good quality stylus brush. This dust can also introduce extra wear to the grooves of your records, so make sure you keep it clean. If there is some harder to remove bits of dust, then I merely brush a little more vigorously, but be careful not to damage the stylus. Never use anything abrasive on your stylus tip!!
In a perfect world we would live in a dust free environment and wear sterile white gloves whenever we touch our records, but this certainly isn't possible so the best way is simply to make sure that you never touch the playing surface of your records. Ever. Keep the records in a good quality inner sleeve, inside the original cover. Make sure the sleeves open side always faces upwards when stored so that when you remove it from the outer cover the record does not fall out. Then you can carefully remove the record from the inner sleeve by only touching the edges and the label. With a little practice it becomes very easy and for me it is second nature, I do it without even thinking about it.
If you follow these simple steps your records should stay in good condition and provide great quality sound for years to come!