Wait for people to contact me: When I bought my two domains, I didn’t pay the extra $12 for Domain Privacy, learn about Domain Privacy here, so anyone can look up the owner of IHateCold(.com) and ReallyFunnyJoke(.com) in the ICANN WHOIS Database. It can tell you whoever owns any website unless that domain owner pays for domain privacy. So if someone was really interested in any of my websites, they could look me up and shoot me an email about their interest.
Control your expectations and keep them based on facts, data and expert opinions. Use a tool like EstiBot to get a general idea of how much the domain may be worth. Do understand that this is an automated appraisal tool, so take those numbers with a grain of salt. However, it’s great to get you started. You can also use paid, human-based appraisal services from Sedo and other providers, but these can get costly. If you’re not careful, you could easily overspend on such services and then realize your domain may not even be worth the appraisal fee.
The easiest and least time consuming option is to 301 redirect the old domain to your existing site. This tactic obviously works best if both sites are in the same sector and are targeting the same keywords; otherwise, if you have a pet supply site and you buy an old Texas Hold 'Em poker site, a redirect probably might raise some eyebrows among the search engines. If, however, your site is brandnamepets.com and you buy onlinepetsupply.com and 301 redirect the domain over, you're inheriting a lot of topical and appropriate links.
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.