Amazon in my experience is one of the best places to buy the books when it comes to price. The books are almost always constantly on sale for 20% or 30% off.

It also depends on his role. Is he mostly just a player? An aspiring DM? Either way, if he already doesn't have it he should have the players handbook. Probably the Dungeon Masters guide, and a few others. The top books I'd say he should have (in order of priority) are probably:

1) Players Handbook 2) The Dungeon Masters Guide 3) The Monster Manual 4) Xanathar's Guide to Everything 5) Volos Guide to Monsters 6) Mordenkainens Tome of Foes

There's also a bunch of other books and adventures, but these are most important. For adventures I highly recommend Tales From the Yawning Portal, Ghosts of Saltmarsh, Curse of Strahd and Storm Kings Thunder.

Now, if you want to make the gift more special, there are a few of the more prestigious (or at least cool) items.

The Rook and the Raven makes superb notebooks. I use them, my wife uses them. I highly recommend them. They are a bit pricey for a notebook, but they are well made, disco-bound so you can add pages and customize your layout, and there are pages with special prompts to help you brainstorm and organize. Whether you are a DM or player, I highly recommend them. Start with either a player diary or DM planner, then go from there. Warning, your skills order these right away. They makes each book custom from scratch, so fulfillment can take a while (sometimes 8 weeks or so). https://shop.therookandtheraven.com/

Want to get him the books, but make it a bit more memorable? Get the Core Rulebook Gift Set with Limited Edition Covers. Very nice looking, has the players handbook, Dungeon Masters Guide, and Monster Manual with special edition covers, as well as a special edition Dungeon Masters Screen. You can find it on Amazon (see link below) or sometimes at your local game store. Dungeons and Dragons RPG: Core Rulebook Gift Set Limited Alternate Covers https://www.amazon.com/dp/B07HFG969C/ref=cm_sw_r_cp_apa_i_IiERDbMK8RT3K

Dice. Dice. Dice. Players and DMs alike love Dice. Especially cool or special dice. You can look around on Amazon for large sets of regular dice (Wiz Dice Bag of Devouring: Collection of 140 Polyhedral Dice in 20 Guaranteed Complete Sets for Tabletop Role-Playing Games - Solids, Translucents, Swirls, Glitters, Alchemic Oddities https://www.amazon.com/dp/B01KP4T6TQ/ref=cm_sw_r_cp_apa_i_rlERDbMH5C6AB), miniature dice (Wiz Dice Halfling's Haversack - 140 Mini Polyhedral Dice, 20 Colors in Complete Sets of 7, Miniature 10mm Pocket Size is Portable and Great for Travel https://www.amazon.com/dp/B07BWK7HVB/ref=cm_sw_r_cp_apa_i_HkERDb6P484G7) or some sets of special material dice, like metal dice (TecUnite 7 Die Metal Polyhedral Dice Set DND Role Playing Game Dice Set with Storage Bag for RPG Dungeons and Dragons D&D Math Teaching (Shiny Black and Blue) https://www.amazon.com/dp/B07CVT3RZR/ref=cm_sw_r_cp_apa_i_GmERDbQ090HDB). I would also check out Artisan Dice. Very pricey, but VERY nice. There are some dice from here made from ACTUAL stones like Malachite, and some even made from Bison Horn.

If he's a fan of Critical Role you should of course check out their Merch Shop. Plenty of cool items there, like apparel, maps, tankards, etc. https://shop.critrole.com/

If he likes using digital tools at the table, you can always get him a subscription to D&D Beyond. It can be a very useful, intuitive tool.

There's so much out there, it's hard to choose. And everyone has different tastes, so its hard to make specific recommendations. If you have any questions, let me know. Getting new players more involved in the hobby is one of my favorite things. And honestly, you sound like an awesome mom. I would have loved for my mom to have supported my hobbies like this when I was younger, and it's impressive the kind of research you are doing. Hes a lucky kid.

Edit: Just remembered a few more things. Reaper makes excellent miniatures he can use in his games, and mini painting is a great hobby he can get into. Check out Reaper Miniatures (https://www.reapermini.com/) and some sets of paints. I recommend Vallejo or Citadel for paints, but Reaper also has some nice starter kits. For tutorials, have him look at YouTube, especially channels like Goobertown hobbies, Miniac, Black Magic Craft, etc.

Also, right now Reaper has a kickstarter going on. They've done this a few times before and it's been quite successful in the past. It's going in now and will end Nov. 1st. Basically, you pledge a certain amount of money and they give you a TON of minis at a much lower cost per mini. I think the core set is like $120, but I think you get well over a hundred minis, so it's a great value. If you don't mind waiting on the actual gift (fulfillment is expected around Feb 2021?), it can be a great way to quickly get a ton of cool minis. Reaper Miniatures Bones 5: Escape from Pizza Dungeon, via @Kickstarter https://www.kickstarter.com/projects/reaperbones5/reaper-miniatures-bones-5-escape-from-pizza-dungeon?ref=android_project_share