House hacking a duplex as a start sounds like a great plan. That's what I would have done if I had thought about REI earlier in life. Having a tenant reducing your monthly payments will allow you to save even faster. You'll learn to manage tenant quickly. Telling applicants the landlord will live under the same roof tend to weed out most bad tenants. Personal home ownership will help you understand investment property maintenance. There are many advantages to your plan.
I don't know why people tell you you're not ready to buy a home. You've finished school, got a career, saved up enough money. Saving 100k after 3 years of starting a career doesn't sound like financially irresponsible person to me. So what doesn't qualify you as ready? For a buy and hold strategy like yours, time in the market is better than timing the market. The earlier you start, the quicker you'll get to your goal. Just make sure you know your market well enough. Conventional usually require 20% down. FHA would get you in much faster with leftover cash to start saving for the next one. Remember to account for mortgage insurance in your calculations.
After the NY duplex I would go to Jersey. It's far enough for you to practice long distance investing but close enough for you to travel quickly should you need to. After that it doesn't matter if you go to TX or FL first.