Dungeon Craft Volume 1 could be a great start. It's a huge selection of terrain, and even has some monsters in there. The biggest downside is that you have to cut out the pieces.

I also love Arcknight's flat plastic miniatures

So if you don't mind me doing some self-promotion -- for a few years I made my own tokens and now I'm selling them online. I can recommend "abstract enemies" for reusable enemy sets, and "customize!" for tokens for your players with the names printed on. I'm actually planning to do some reorganization of the site a little later today; the custom names for player tokens is a new thing and not too well-represented on the site currently. If you want those but can't figure it out on the current site reach out + I can hook you up.

For the rest of it, I would agree about Chessex mats + either dry or wet erase markers (dry erase markers are honestly fine for most situations in my experience and a little easier to clean up). I never used the terrain tiles or anything, just drew on the mat; I think it's up to you -- the only thing I'd add is that for certain spells you may want to get some circular overlays to represent areas of darkness / spherical area effect spells since that one comes up frequently.

I didn't want to invest in figurines, as there's always some new monster I want to use and would be frustrated not to have a figurine for. So, what I picked tools that lean on everyone's imagination:

• Acrylic character tokens from https://www.c4labs.com/product/set-of-three-gigantic-monster-character-tokens-for-rpg-and-tabletop-games-color-options/ . These are fairly cheap, and you can write on them with wet/dry markers to differentiate characters.
• A blank gaming mat from https://meleemats.com/ and a bunch of markers. I draw fast/simple environments to battle on instead of worrying about printing something with amazing detail, or buying a bunch of models.

Hope this helps!

I think your instincts are good, I've been playing D&D and other RPGs since I was a kid, and that's pretty close to my setup. Here's a couple more things you might want to consider:

DM Screen

A cardboard partition between you and your players. It's useful to keep your notes and dice rolls hidden from the party. There's a lot of variety out there in how people customize their screens. There's official versions which have reference rules printed directly on the DM-side of the screen, and if you're still learning the game you might find that very handy. You can also feel free to stick your notes directly onto the screen with sticky notes or paperclips or what-have-you. You can absolutely make your own out of posterboard and some printouts if you're looking to save some money

Initiative Tracking

I've found it's helpful to have some kind of visual for the party to see when their turn is coming up in initiative. YMMV since you only have two players, but generally speaking the larger your group is, or the more dynamic the encounter is, the more important this becomes. In my experience, it helps my players be prepared for their turn when they can see that it's coming up soon.

There's plenty of ways you could implement this, and they range from high-tech apps to just simply writing it out on the battlemat. What I've done is glued cardstock labels to clothespins and then pinned them to the DM screen. This is also pretty handy for me, because on the Player side it shows whose turn it is, and on the DM side I've had my players record things like their Passive Perception or AC so I can reference them and speed up play. You can look up "initiative flags" or "initiative tents" for more inspiration

Condition Indicators

These are little rings that you can place under your miniatures or tokens to show that they are suffering from some sort of condition (grappled, invisible, stunned, etc). I find them really helpful because I run for a large table, and love large encounters, and all of that becomes hard to keep track of otherwise. You can buy condition rings that come with a large set of every possible condition, but you could also just slip a piece of paper with the condition written on it under the affected token.

Good luck on session two!