It's a good idea to research thrill rides initially, this without forgetting that some guest prefer less intimidating rides. A small, custom built shuttle loop is a great way to attract a large number of guests and filling the park's wallets. Of course, maximum train & queue lengths, and an on-ride photo section are must-haves on every succesful coaster.
The sloped landscape in Pokey Park allows the good ride designer to build many rides underground, and cheaper than on flat terrain. This is a good way to maximize space. It is possible to beat this scenario without expanding, but much easier to do so. Players are however only able to buy construction rights to the land across the road, and it is important to build several footpaths to connect both sections of the park. A Chairlift is useful too, as it doesn't need much space, goes high and is cheap, yet attracts guests and boosts the park value. Also, players should stay aware of depreciation (the fact that Park Value slowly goes down over time), especially those who play in RCT1.
It is possible to beat this scenario without buying any additional land or construction rights, although it is very difficult. There are three areas in the park that can be good station platform zones: behind the Carousel, along the fence by the Spiral Slide, and in the space above Purple Peril along the park fence. These three areas can serve as starting points for coasters before going underground. Alternatively, coasters can be made entirely underground, requiring only one opening underground for the entrance path.
If overcrowding becomes a problem (when guests complain and say "It's too crowded here!"), then wise players will start to build paths above the park rides and around the park. Despite not immediately needed, the additional path network will maintain a higher park value by lessening the guest overcrowding. Obviously, food courts are to be avoided here at all costs, since they generate overcrowding.
The cheap way to beat Pokey Park is to close the park and the rides, get rid of everything and start flattening the landscape before starting it from scratch, building everything tight and smart. It is cheap and much less rewarding than succeeding while keeping the original park up, but it works.