You’re not going to find SSBs, TMBs, Pika Trophies (97-99), or anything like that in this price range. However, that doesn’t mean you’re out of luck. There are a lot of really nice and very rare cards under $2000. If you are going for ranked prizes then you will have trouble. Many participation or winner prizes from regional or city events are available at reasonable prices.
1.Many of the legend-era prizes(2010-2012) are priced under $500. While currently not the most popular era of the tcg, these are a bargain for what they are. I’m not too knowledgeable but there are people here who know a great deal about them.
2. Fan Club prizes represent the accumulation of hard earned points throughout the year. Most of us know the Eevee, Porygon, and Shining Magikarp but there are many more throughout the years. Most of these won’t exceed $2000.
3. Early Prize cards. This one may be a bit more of a stretch as rare cards from this era (1997-2002) are increasingly difficult to obtain in any condition. Getting one of these under $2000 means it will more than likely be damaged. A Kamex Mega Battle Computer Error PSA 5 ended on May 28 2019 through PWCC auction for $1275 which is well within your budget. Just know that competition for these types of rare early promos is extremely high. In this particular auction there were 5 bids over $1000 among 4 bidders.
Quick note: there are good guides for Yahoo Japan search terms in the Articles & Guides section 