Firstly, excellent, I am really pleased you decided to do this mod; and were obviously inspired by my work.
I beleive the Ipaq H3760 was the immediate follow up to the Ipaq 3660 (as per mine). Specs are very similar.
You will need either the "cradle", designed to pop your Ipaq into and connect via USB to your computer; or one of the USB cables for the Ipaq (from Hong Kong typically) to do the same job - without this you won't be able to copy data across to your PDA or install games.
I tried using a NES D-pad originally, but found due to the closeness of the surrounding electronics from the system it was awkward to place, so I used tact switches instead - even then it was only just ok.
I tried upgrading from Pocket PC 2000 to Pocket PC 2002 but found the emulators were not compatible; if you didn't exit in just the right way the game kept running on top of other applications and you couldn't stop it. I suggest you keep to Pocket PC 2000. If your system comes with Pocket PC 2002 and you experience similar problems, the upgrade to Pocket PC 2002 I used allows you to replace the ROM image, I still have the Pocket PC 2000 OS image on my computer.
I don't know if your Ipaq got over the problem on the Ipaq 3600 series that a button is not registered if you are also pressing a direction button, which cuts out action and shooting games.
I tried to install CalPlus application a while back, but since found it contained a trojan, which explained why I had to cold boot the system (all memory emptied apart from the OS) and start installing stuff again.
Apps - not really found any useful, over and above the ones already in the Ipaq. I used to use a slideshow viewer occasionally.
You will need to use ActiveSync 3.8 - don't use a later version. This works with Office 2003 and XP and Pocket PC 2000 / 2002.
Emulators - iMAME is too slow, PocketSNES is a bit too slow but ok (as I recall), as with PocketGENESIS. GNUboy is am emulator for GB and GBC, although GBC is a bit slow, GB (mono) games run great. One of my vids showed playing Tetris Attack. Basically, action games like 1942 aren't good because of the key button issue; but there are a number of other games which are fine.
MS Gamepack (PacMan, Ms PacMan, DigDug) is good, I installed it (as per pic) and you can run the game with D-pad or stylus.
Sure, you want to make your project smaller, however as the pic below shows you may struggle making the length and breadth smaller than I did (the extra length is for the USB card connection); the only height difference you have to play with is the batteries as you say. AA's are 14mm high, in battery cases about 16mm high. If you use Li-ions you might save as much as 10mm at a pinch and maybe end up with 34mm high. The reason for this is the PDA will be angled due to the components like a D-pad, wiring, etc; also, you need a slight gap above the PDA or it seems to stop buttons working (shorting). I hot glued two strips of mounting board against the battery pack at the base in question, then snipped the card in half, raised the battery pack by 3mm and re-hot glued - works great and reliably now.
I will be happy to give you any advice I can. If you need any of the software I referred to above, contact me, I can e-mail it to you.