Hey @Alvin Smith,
Congratulations on your steps forward into real estate investing and owning your first home! Finding and choosing the right home for what you want is crucial to your future investments. If I may ask, if you haven't purchased your first home yet, why not make your first home your income property? You could househack (Buy a multi-family home and live in one unit and rent the other ones out) and get your mortgage paid as well as some positive cash flow from your tenants' rent payments, but to answer your questions:
1. What are the basics when looking at a property to determine whether it may be good or not?
So when looking at properties, you always want to "do your due diligence", which for a buyer in the financial sense, means evaluating whether you have a deal in your hands or not. A deal in the financial sense of real estate investing is a purchase that will make you money and serve as an asset, not a liability. For buying houses, this means that you want to evaluate whether the purchase costs (e.g. Monthly mortgage & interest, property tax, closing costs, etc.) as well as any maintenance costs will outweigh the potential profit you'll receive from it (e.g. rental income if buying-and-holding, or ARV if fixing-and-flipping).
The best thing to do is to learn and understand EVERYTHING that has to be paid for when buying a house and then using the BP Calculators to evaluate whether you have a positive ROI or not. There's a BUNCH of other things that go into figuring out whether a property is "good" or not, but these are just a high-level overview of the financial aspects of evaluating a good property.
2. What are the different methods to calculate income and profit?
So there's a few different ways to evaluate profit and it all depends on what your strategy is. Do you plan to buy homes and fix them up to sell them for profit, or do you plan to buy homes and then rent them out for continual cash flow every month? The main baseline of calculating profit (The money you keep in your pocket after EVERYTHING has been paid for) is simply:
Profit = Income - Costs
Profit - The amount of money you keep in your pocket at the end of the day.
Income - The gross amount of money brought in from the investment you've made, before any costs are taken out.
Costs - The amount of money you paid/will have to pay in order for you to make an investment.
That's all there is to it, in a basic sense. So long as your Income from whatever method of investing you use is greater than the costs associated with that investment, you will see profit. Now, how much profit you'll see is a much deeper concept. Generally, investors usually go off of a few rule-of-thumb percentage philosophies (Look up "The 70% Rule", "The 50% Rule", "The 1% Rule" for some starter ones) to determine if an investment will give them a good profit. It's all about numbers at the end of the day. Oh, and also the BP calculators can help :).
3. What about lawyers and accountants, are these things to consider on an ongoing basis or as needed?
Okay, so lawyers deal with legal stuff, right? You use a lawyer whenever you have a legal situation dealing with some kind of contract, generally. As a real estate investor, you typically only get involved with lawyers as needed (e.g. closing a purchase, evicting a tenant, etc.) It's always good to have a reliable lawyer who knows real estate laws in the state you invest in as a contact, but you won't be constantly calling a lawyer every week.
Accountants, in general, are even less frequent than lawyers. Again, it's always good to have a reliable accountant who knows real estate on your team, but accountants usually come of use around tax-season (So that they can give you all those sweet tax benefits). You typically won't be calling your accountant every week, though.