In theory, you could technically acquire a domain for $10,000 and be able to sell it for $100,000. You could also acquire a domain for $10 and be able to sell it for $100,000, $10,000… or $100, you get the picture. Because of this, it’s hard to recommend a perfect starting budget because your strategy, experience, and the pace at which you learn will hugely affect your buying and selling decisions.
They see a domain’s price tag and they can instantly tell whether it’s under or overvalued. This is probably the most important skill one should have in this industry. Neil Patel has an interesting related quote: “The most important thing to remember when buying sites is that you always make money on the buy, never the sell.” In order to successfully do this, you must be able to spot undervalued domains. This is what will ultimately translate for you into a handsome profit margin when you get the opportunity to resell the domain for its “real value”.
However, I'd argue that most people in the business really struggle as they don't understand what makes a good domain name and what's a bad domain name. While I do not work in this field full-time, I can say that I can make a living of it, but it's probably because I don't ask for absurd prices (e.g. domain name for $8000 is just unrealistic and won't happen) and therefore can sell domains easier. 

That said, my recommended budget for beginners would be $500+. Using this budget you could buy a bunch of high-potential $10 domain names, expired/dropped domain names or a mix of both. It’s very important to invest only what you can afford to lose and treat this as a side hustle till you get the momentum going. As you gain experience, industry expertise and some sales under your belt, you can then consider slowly growing your business into a full-time gig.