Congratulation @Neil P. The first purchase is a huge step. There are a number of factors involved in your question that I will do my best to address. This turned into a novel, so I hope it helps. =)
#1. Can I buy and keep my 1st place?
There are a handful of factors if you are buy 1-4 unit properties: a) Debt to Income Ratio b) Downpayment + Reserves c) Credit.
The bank will accept up to a certain amount of debt and then cut you off. Get with a lender to explore how much more borrowing power you have based upon your income and current debt load.
Until you have 2 years of rental income on your tax returns, you don't get to count the properties cashflow as part of your income (and even then it is only 75%). This may be a bigger or smaller issue depending on the cost of the properties you are looking at,
The bank will expect you to keep reserves both for your personal expenses as well as your rentals. The more properties you have, the bigger a pile of cash they expect you to sit on. That said, I have often been able to leverage retirement accounts to offset that requirement.
Lastly, this is perhaps a bit early, but every time I do a deal, my credit gets a ding. And we seem to do enough deals that no matter how hard I try, I can barely eek out a 740 credit score. We are financially perfect in every other way, but I am constantly taking out loans and have millions in property debt. It makes me look like a risky consumer, and despite the fact that this is a retarded measurement of my ability to be a good investor, it is a real challenge in getting the best rates. Not a show stopper, just a detail worth sharing.
Note that a lot of this changes when you go with 5+ unit commercials loans.
#2. Should I sell?
The answer depends on: a) is this a good buy and hold OR do you see the market having significant upside in the near future, b) are there unique opportunities that selling this property enables you to take advantage of, c) how does this property fit into your lifestyle / family plan?
I often struggle with that question. When I started, I was going to hold these homes FOREVER. They were going to my kid's, and a couple still might. But my wife and I quickly realized that at our age (we bought our first rental when I was 27), leverage was in our favor and right now mortgages are seriously on sale.
We decided that we would either cash out refi or 1031 into better deals to keep our leverage working in our favor and increase the footprint. Our properties had to have enough cashflow to safely cover themselves, but beyond that, we didn't need the cashflow right now. We had read Gary Keller's millionaire real estate investor and had a high level game plan of "control a million, own a million, earn a million". I'm pretty stoked that 7 years later, through careful acquisitions, we are starting to position ourselves for step 3.
When I consider whether to hold a property (we are under contract to sell our 3rd rental purchase right now), I took a look at my investment philosophy and decided that this property was not the best leverage for my equity. It is a SFR that has gone up 65% in three years. We made our profit from this market, and while I am not sure if we are at the top, I don't see a whole lot more upside. The home was due for some large capital improvements (roof, plumbing...). It would be a fine long term hold, but with that equity I can control an apartment building that has 3-5x the gross rents. So I am hunting for the right fit.
I am also loosing interest in managing our properties personally, and while we probably have enough room on the home to pay for a property manager, it would wipe out much of the cashflow. Heck of a SFR equity market, but not so hot on cashflow (and the reason I didn't cash out refi).
Summary
I would analyze the market and see what deals you can identify. They I would talk to a mortgage professional and learn about your buying power using some of these deals as a metric. That will give you real context upon which to base your decision.
Best of Luck (and give this a vote if it was helpful).
