Welcome onboard, it's in the perfect place!
Lovely. Running from the early hundreds up to about then is such a wonderful period of White Dwarf, very much their period of transformation and growth. That's a collection to treasure.
Whilst many of us are in the "play with the toys" camp on this occasion I would say if you have good condition White Dwarfs with their cover models intact and card inserts intact I would keep them that way. Whilst White Dwarf magazines are not rare as such those that are fully intact are considerably more so and so I'd probably keep these that way.
As to looking after them in general as a minimum with all my magazines I pop them in poly bags. So any good comic shop (and there are some that sell online as well) will have bags for comics and magazines (in various sizes!) that will offer some shelf/box protection for the magazines - simple enough to use - you pop the magazine in fold over the flap and seal with a bit of tape (I like to use Scotch "magic" tape since it has a much better shelf life than sellotapes). So they end up looking like so:
View attachment 19705View attachment 19707View attachment 19708
If you want to up the ante in your storage you can get better quality bags - as Knight Girl already mentioned - made for longer term archiving in Mylar and so forth, and also card backing sheets that are buffered with calcium. Papers contain acids and these acids eventually degrade the paper, having an alkaline "sump" (ie the calcium buffer) in with the paper helps to neutralise the acids as the leach out of the paper and prolongs its life. The card, like the bag is generally a bit oversized for the magazine so also offers some additional protection for the magazine corners from dings and so forth. However it is harder to find buffer boards for magazines (much easier in US comic sizes) so I'd probably not bother about doing that myself. I ended up finding some buffer boards, but I had to cut them to fit the bags so I only bother for the odd issue:
View attachment 19709
For those with miniatures on the front obviously those are a bit harder storage wise. They can still be polybagged, but if you want to have all the WDs on a shelf or in boxes (generally on their edges for easy access rather than on top of each other) you'll need to pop it in a box, if you're being nice and fancy and want acid free card companies like PEL -
https://www.preservationequipment.com/archival-storage/boxes-trays do a wide assortment of such things. Otherwise given everything is in poly bags you could probably just get away with a normal "large letter" box for posting things to pack it out for storage.
Storage wise - just avoid anywhere damp really. Ideally in a normal room inside the house, so avoiding lofts/attics and cellars! I keep all my own White Dwarfs (1 - ~200) in magazine boxes on some shelves out of the worst of the sunlight, but my collection is by no means mint (having recollected it over the years, my originals being with my brother).
A note - I would not use the A4 paper pockets you get for ring binders in places like Rymans and so forth for storage. Certainly I've found with odd bits I've rediscovered from my childhood that they can end up sticking to the inks on paper and lifting them. Use something designed with storage in mind (and enough bags to last you will only be £10-15 tops).
Well by the time you've read through all those WDs - and do read them! We'll have converted you to the old ways ... and your poor new 40k will be languishing and you'll be hunting down some lovely old lumps of lead!
In all seriousness however welcome to the forum, enjoy your collection and perhaps you'll find some inspiration in some of the old issues for painting ideas and modelling ideas you can take into your current 40k games.