Fill up the remaining places on the grass with some flat rides, add benches and litter bins, and build an Information Kiosk. Remove the flowers and unnecessary paths for extra space. Set your research funding to maximum and direct your priorities to thrill rides. Once you have fully developed the remaining grassy space, start cramming tracked rides on the beach. A Wooden Crazy Rodent Roller Coaster or a Virginia Reel would be a good choice, since both require little space and are relatively cheap to build.
The two rides that must be preserved are incredibly old and, thus, prone to breaking down. Ghost Train is 35 years old, and Woodpecker is an astonishing 68 years old. While both attractions suffer from high down-time, Woodpecker is always at risk of a Station Brakes Failure crash in its starting configuration, so setting the ride to run six 3-car trains or one 12-car train as soon as the scenario starts is recommended to remedy this issue. Make Ghost Train free to ride if you are charging a gate fee, and charge no more than $1.00 regardless for Woodpecker. (You can get away with charging more for Woodpecker in RCT Classic, but be careful.)
Once you have repaid your loan and filled up all the space, start expanding your park slowly. The hills around the park are a good spot to build tracked rides partially underground to increase their excitement ratings and possibly make them indoor rides. It might be necessary to set research to roller coasters only for a short period of time to help you build the big ticket rides you need to meet your guest goal. That said, if you find yourself falling slightly short of guests toward the end, you can always advertise.