First off, delete the big path rectangle in the middle of the park and the buildings to reduce the chances of guests getting lost and to make an extra $1,000. Then, you want to build every single thrill ride and gentle ride (no tracked rides like the Car Ride). Since the park entrance fee is free, you should try to jack up the price to all of the rides to the maximum guests will pay (if a ride's excitement is 4.87, you can make the price $4.80 and still get the guests to ride that ride). Also, you'll want to set the research funding to maximum, and set roller coasters and shops and stalls as priorities. Until you get get the First Aid Room, you'll have to hire far too many handymen (not to mention guests will complain that they're sick); and guests quickly run out of money without having a cash machine.
When you first start seeing throw up around your clumps of rides, hire a few handymen and mechanics. When this happens, this means that your ready to build your first roller coaster. Since the excitement has to be over 7, it would be good to keep your track to not be close to each other so you can fit lots of scenery and paths around it to bump the excitement rating up. Make sure you make lots of block brakes and stations (optional) so you can fit many trains on one ride. Make sure your queue lines are not too long, but not too short. When you finish your roller coasters, make sure you charge enough (no less than $5) so you can make a profit to make another roller coaster / ride. Once you have the First Aid Room and Cash Machine, you can uncheck shops and stalls from the priorities and (optional) reduce the funding to normal.Most of your roller coasters will be custom, so try to make them either very compact or interweaving. Also, build underground to save space. There is no time limit, so it's just a question of how long it will take to complete. Also you can use the mountains to boost the height on shorter roller coasters (like the Corkscrew Roller Coaster).