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.
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.
There’s an important distinction to make here between domain flipping and website flipping. The latter mainly refers to buying and selling full websites. By full websites, I mean websites that actually have content and more often than not have traffic and revenue. When buying and selling websites, the domain name matters less as the main value there is the content, traffic, revenue, history/reputation, sustainability and growth opportunities. The same can’t be said for domain names where you’re just selling “the name” and hence it’s all that really matters.