Motorized zoom and focus are premium features. Once a projector is properly setup, there's zero reason to adjust those items except for periodic maintenance. For example, with a good ceiling mount, I only touch my projector about once every 6 months, maybe less, to fine tune it only.
I'm not sure how tall the ceilings are, or your screen size, or your mounting position. I'm guessing you still have an older 4:3 screen that you are using, so going to a widescreen projector wouldn't work.
This is the list of models which meet your criteria...
Be aware that the first model listed is a typo for pricing and is over $5,000 online, not $483.
The sort allows for searching on motorized zoom, but not motorized focus, so you would have to double check that yourself.
All projectors (ALL!) can be ceiling mounted, you just need a decent ceiling mount.
If you are touching your projector regularly to align/focus it, then something is seriously wrong with the installation or the projector.
Frankly, if you are on a budget, I would get a good ceiling mount that's very sturdy and locked into place. Then I would get a manual zoom/focus projector and lock it into place with that mount and you will save hundreds of dollars and get a solid solution for the money.
The Chief RPMAU mount is excellent, and works with standard 1.5" piping so it can be mounted correctly where you need it.