Hi @Austin F.! Mind if I ask why you chose that specific area? Is that where your sister lives?
Some things to consider with your mom: number of beds? baths? square footage of home? sq ft of lot? number of floors? basement required? backyard requirements? Is next to a busy street OK or would you want something quiet? Are you willing to do work on the house or is move-in ready required? Maximum budget (more on this below), parking requirements?
There's single family homes, townhouses and condos yet not many multifamily buildings. You're better off buying something right sized for your mom and using the remainder of your money as an investment, rather than trying to combine the two. Your mom may not want to live in the best investment, conversely your best investment choice probably isn't a place your mom wants to live.
Regarding budget, you really have to look at monthly PITI (principal, interest, taxes and insurance) rather than just purchase price. Taxes vary so much that a $350k house might have the same payment as a $500k house with lower taxes. So the purchase price matters for your down payment yet the total monthly PITIA (A for association in condos, townhouses, etc.) will affect your DTI (debt to income) which will affect your ability to get a loan.
If you do lean towards condos/townhouses then set a limit to what you'd pay towards HOA compared to the amenities covered. I was looking at condos/townhouses a few years back and I think I got down to like $400-$500 is the maximum I'd pay, so I'd set my filter at $450-500 for HOA when browsing. Essentially, I don't care if you have a doorman and a shoe shine, I won't pay more than $500 for the HOA so let's not waste time looking at those properties.