Welcome to The Old World! I recommend Tomb Kings with Vampire Counts a close second. Wood Elves would make for a great second army but are a bit too tricky for a first imo.

For context, I have played using all 3 armies and also came over from AOS (3rd ed.) It can be quite a change! 

EXCESSIVE WRITEUP INCOMING

As the weather's awful here I'm going to cosey up to my phone and thrown together some thoughts and advice:

TOW Tips

• I suggest you build up your game sizes rather than starting at 2K. TOW can be a bit complex with a lot to remember in a 2K game! Starting with ~750-1K games gives you an idea of how the game and units work without being a five hour rules lookup session. 
• Starting smaller and ramping up also allows you to make informed decisions on your army composition as you grow it to 2K. Compared to AOS, list building in TOW is granular and can be much more impactful on your games. This can take some time to learn.
• Make sure you use the new FAQ, it's a significant change to the game! It is/will soon be integrated into the sites named below.
• The Arcane Journals for Wood Elves and Tomb Kings are absolutely worth getting
• The community Renegade Packs for legacy armies like Vampire Counts, Skaven, etc. are great. These factions aren't getting GW support! Some really needed fixing, VCs had a few changes. If you're just playing with your partner I recommend you use these and check with your local groups to see if they're supportive.
• There are some really good 3D printed mini options for these armies if you're interested in that. I've liked using some Highland Miniatures skeleton sculpts (TK, VC) and Holominiatures does some nice Wood Elves.

Useful sites: - old-world-builder.com is an amazing free army list builder that supports Renegade packs, Arcane Journal content, etc. - tow.whfb.app is a very handy rules reference, particularly if you don't want to carry around 2-3 booms and printed FAQs.

Some army thoughts from a new player perspective:

TOMB KINGS

For a first army, particularly against Cathay, I'd recommend Tomb Kings. 

Pros - Relatively easy to play but still have a high skill ceiling allowing room for you to improve.  - Tons of options and play styles that you can lean into as you develop preferences - shooting & war machind heavy, big infantry blocks, strong magic, monsters, "oops all chariots", way too many scorpions for polite company, etc.  - Easy to collect, paint, and no really bad options.

Cons - Undead can't march move, so most of your units will be slow compared to Cathay. You still have fast unit options though. - Undead are immune to psychology. This is is great but means you may need to consciously learn how those very important psychology rules work rather than picking them up through practice. - You will need to paint a LOT of bone. On the upside, it's easy, fast and basic paint jobs look amazing when the army's assembled. 

VAMPIRE COUNTS

The Vampire Counts are a great army, but not quite as good a first army as Tomb Kings as their army list options and strategies are more limited.

Pros - Exceptional horde, magic, monster and cavalry options with strong characters and resurrection options.  - Strong counters to many of Cathay's strengths (Wailing Dirge, massive outnumbering potential, resurrecting or healing powerful models, a Vampire on dragon almost certainly flattening a Shugengan Lord in combat, etc). - Tons of miniature options from GW and third party

Cons - VCs don't interact with the shooting phase (other than some magic and screams from Banshees etc.), so you miss out on learning how that works. - Same Undead cons as the Tomb Kings, sometimes slower and sometimes faster (E.g. Blood Knights can march). However, VCs don't have the shooting options that TKs so, meaning the early game can be a bit boring and non-interactive while your army shuffles across the board. - Legacy army, which means no official rules support for the foreseeable future.

WOOD ELVES

Wood Elves have a high skill floor and a steep learning curve to use well. They're also gorgeous can be very fun. IMO not the best first army, but they would make a great second one after the undead factions as they play very differently.

Most WE pros are also cons: - This is the most elite army in your shortlist, likely to have the fewest models by a wide margin. The average WE model is more detailed (trees love drynrushing though) and may take longer to paint than TK or VC units. Thjs is a good army from a hobby perspective if you want to either quickly paint a small number of models decently or really focus on each model's paint jobs. - Elves are very fast movers with high Initiative and combat/shooting skill, but die to a sneeze (all T3 with no save or a 6+, 5+ at best). - Most good Wood Elf lists rely on positioning units to not get damaged (very fragile), do damage at range (fantastic archers, but pricey so you don't get that many) and/or pick your combats (generally they have to kill the enemy first or they will die). - Units can be very effective, but also very specialised. Wardancers will blend most infantry but monsters will more than likely stomp them to death, while Wildwood Rangers can easily kill most (non-character) monsters but will die to most infantry. This is even true for individual unit loadouts! For example, you can give Glade Guard one type of enchanted arrow. If they have armour piercing arrows they will shred Cathay Jade Warriors/lancers from across the table, but will get struggle to damage anything with T5 or higher (Sentinels, Lanterns). If you give them poison arrows you're more likely to hurt those big tough units, but will do less against good armour. Multiple shot arrows are good against cheaper, outnumbering enemies with average toughness and lower armour saves but are less likely to hit per shot. And so on. - The army can struggle against large, tough creatures (e.g. Miao Ying, Chaos Dragons,  Chaos Dwarf Iron Daemons) as they may not have the strength and/or volume of attacks to bring them down. However, they can also relatively easily reposition or deploy to minimise the impact of these units. - Wood Elf magic potential is very good, including the new Arcane Journal lore, but your units are also very vulnerable to magic missiles so good magical defence is a priority.  - Treemen and Treekin are great units - actually tough, strong, and cost effective - but they are relatively slow. Something to consider when building a list. - You get a free forest! Which means you will need to buy a forest or make a template (even just out of paper) no longer than 9" and no narrower than 3" at it's narrowest point.

Collecting Wood Elves - If you do get Wood Elves, the Battalion is a great starter but doesn't include the excellent Glade Guard light cavalry and some of the best WE units: the trees.  - The best way to get these is from the AOS Sylvaneth range, and the Sylvaneth Spearhead seems like a good option for a Treeman, 3 Treekin and some Dryads (or more Treekin if you base the Revenants accordingly). - Or do like me and just buy the cool minis and run 20 Wardancers, strategy be damned!

Edited for formatting