You want to be careful about taking on a small multi without reserves, and what you have now is basically zero reserves. Real life story: I helped my sister buy a four unit property this January. Remember that hail storm last week? She had actual holes in the flat roof from that, with massive water damage and two units currently uninhabitable. Yes the insurance will pay for the bulk of it but a typical hail deductible is $2500 and there are a lot of other costs that will be incurred.
What would I suggest? Sell your car, buy something used, cheap and practical that will last you a few years.
Buy a 2bd 2ba condo somewhere convenient to your new job and get a room mate. Look for something that will have some modest cash flow when you move out. Renting is going to be pretty much as expensive as buying right now, and this way you can be getting in the game and not tossing your money away on rent. I suggest a condo because rather than an SFR for a couple reasons. One is the reserve fund scenario. With a condo your costs are much more predictable- any major issue like a roof or a sewer line will be covered by your HOA payments. Another is that it's actually a lot easier to find a cashflow condo than a cashflow SFR in the area right now. And finally, a condo you can afford will be a lot nicer than any house you could afford on your current budget.
In a year or two you can move on to another property and keep the condo as a rental or sell it depending on the market and your long term plan.
You are totally on the right track. I wish I had been thinking like you when I was just out of college!