Ivory Towers is an extremely huge park with lots of space to build rides and attractions. This is a peculiarly hard scenario at the start because you must fix everything before anything else and if you don't do it properly, you might have a disadvantage in time.
You should pause the game immediately and hire lots of handymen and some security guards, placing them throughout the park. Take the opportunity to set your research properly and adjust the settings and pricing of the pre-built rides. There is really no reason for demolishing any of the rides, maybe except for Hurricane/Force Nine (the Suspended Roller Coaster). The Monorail is a good transport ride for such a large park and has a reasonable Excitement Rating. The Boat Hire can be redesigned if you want to, but there's nothing wrong in not demolishing it. As for the coasters, they're reasonably well designed; they're not spetacular but will be your main source of money at the beginning.
Right after you unpause the game, make "Tree Topper", the Steel Mini Roller Coaster, have only one train as it can break down with Station Brakes Failure (or then set a safety mechanic patroling the exit and add brakes before the station). Then, while your handymen handle the huge amount of litter and vomit, start replacing the vandalised objects throughout the park and make sure to place bathrooms, food and drink stalls in every area you feel the need for them.
The Suspended Roller Coaster is really too intense and if you really want to, you can remove it. The good thing about doing so is that the back area will be a lot emptier and easier to build in (building coasters or even pathways can prove to be really tricky because of the height measurement of this type of coaster. With the money you get for it, you can build a new roller coaster in the same place easily. However, if you change the trains on Hurricane to two cars, it will be less intense due to reduced velocity, and should be a popular and profitable coaster. In the event of a Safety Cut-Out, however, you may run across stalled trains at the end of the track. In one way or another, if you remove it or not, it shouldn't become a problem.
Once all that is done, you can start building some rides. Begin by building some gentle and thrill rides around the park. If your hired staff are taking too much out of your pocket, go ahead and sack a few of them, but leave enough around to keep things in check. Be sure to hire a few mechanics as well. After you recover mostly from the problems, you might build another coaster, preferably a cheap one. This will bring in more guests and increase your park rating. Also, have in mind you can use the "On-Ride Photo Section" for extra cash.
The terrain is quite hilly and you'll have to build rides very wisely, having good sense and planning things out. At some point you should think of your path infrastructure as your guests can get lost at the back area. Just try to make more intersecting pathways, creating a nice net system (of course, not too overdone) over your park.
Getting 1,000 guests shouldn't be a problem at all, but in the worst case you can start one or two advertising campaigns at the end of Year 3.
Differences in RCT Classic
Completing this scenario in RCT Classic works a little differently. The immediate litter/vandalism fix is more challenging, because the game unpauses the moment you add a staff member or repair a vandalised object. However, it's also literally the only urgent problem you face, because Tree Topper has block brakes already added and so you don't have to worry about it crashing.
These two both increase the incentive to remove the other coaster; Tree Topper will still be operating at high capacity with no fear of a crash, and you won't be paying much in loan interest during what will be a longer path repair phase in game time than it would be on desktop. You could even start an advertising campaign right after the clearup phase to try and swamp your old unhappy guests with happy new ones, helping your future cash flow for a second coaster later.
Note that there is one tile of track between the block brakes and the station. If you want to remove this to extend the station and increase capacity, you must modify the hill leading up to the helixes where there are currently block brakes at the top, because longer trains will slide backwards out of those block brakes.