Think of ways that the domains you buy would be a valuable asset to the buyer. Picture someone who would benefit from buying the domain in a space you are very familiar with. If this was you and someone was trying to sell you this name, would it be beneficial for you to own? Be honest. If so, why? If not, why? Use those answers to refine your search for names.
Yes, buying existing domain names can be profitable too. Existing domains with a potential for profit can be found using Sedo. Make sure you pick domain names that have good traffic, backlinks and Google PageRank under 17 characters. Also, steer clear of existing domain names containing special characters or numbers because they are not likely to be sold.
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.