Search on here and BiggerPockets.com for the 50% rule. You should be getting about double in rent what your mortgage payment (principal and interest part, not counting taxes and insurance, which are likely part of the payment) is to be break even. Anything more than that is profit.
That's with 0% down. If you're putting money down (which is a good thing) you should be getting even more profit. That is, if you have to put down 50% to force it to break even, you're forcing cash flow and not actually getting a good return.
This makes me think it's quite a bad deal:
I would end up renting out the home for probably more than my mortgage payment would be - at the very least the rent payment would cover all but a few hundred dollars a month of the mortgage.
You may just be in a place where owning doesn't make sense based on price to rent ratios. Fitghting it is just asking to lose money (or way underperform wherever that money could be invested).
Or I could invest my savings and hope to get a decent return - I don't really see getting anywhere near 2500 a month in returns though...
I don't see you getting anywhere near 2500 in returns on this either.. Unless (hypothetical numbers) you're renting out a mansion for 10,000 per month and the mortgage is 2500. (10k rent - 5k expenses/vacancies/capital repairs/etc - 2.5k mortgage = 2500 profit). That's an exaggeration in this case (you likely won't see 5k/mo, however a vacancy at the 10k/mo range hurts you bad when it's empty and is a lot harder to fill, so it likely isn't that far off).
This deal sounds more like you'd eek out a break even (if not negative return). If it was break even, then you could come out ahead via mortgage interest deduction, depreciation, equity paydown, and potential appreciation. Otherwise, you'll likely be losing money, and I can tell you a few places where you can beat that return.
Bottom line: there are places that just don't make sense to invest in real estate. You likely live in one. If you want to invest in RE, you'll probably have to go out of state.
/disclaimer: I wouldn't invest in most of CA, but I am involved in a few REO deals there currently, that will likely be rehab / flips, although buy and hold is one potential exit strategy, not plan A. I am involved in these due to bank contacts, and would not be normally investing in houses on the MLS in CA.