The third option is the one that's the most time consuming but also has its benefits. It's like having a successful restaurant and buying another restaurant and operating them simultaneously. They're not the exact same restaurant, but both are popular in their own right and make you money. The same goes for Option #3. You could update the content on the old domain and sell the same products that you're selling on your current site. If you can get both sites to rank alongside each other in the SERPs, you're increasing your conversion chances and sales potential.
Use the advanced search option to quickly hone in on the type of names you are interested in. You can narrow the results by price, top-level domain (i.e, .com, .net, .org, .club, etc.), keyword, and many more filters. Using this feature will help you quickly sort through the millions of domains on the aftermarket and find the domain names that best fit your end goals.
Since search engines regard inbound links as recommendations, these links have a decisive influence on the ranking. The search engine definitely doesn’t appreciate link networks and won’t give new projects a jumpstart by allowing a former website’s backlink profile to be used when registering a new domain. Using an expired domain is like playing with fire, where the worst case scenario is that you’ll be penalized or be excluded from the search index.
You can still buy two word or three word domain names incorporating your target keywords. Moreover, there are millions of domain names out there which haven’t been used at all and are bound to expire soon. All such domains keep coming back to the domain marketplace. What more, there are useful tools available to research and filter through such expired domains.

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.