The key to free parks is to pace yourself, build coasters, and make SURE you get the cash machines.  I would even suggest trying for the cash machines as your first research.

This is how I approach them:

Get cash machine.
Research only thrill rides.
Research only gentle rides.
Research rollercoasters/water rides/junior rides

Charge 1.50 - 2.00 for thrill rides
Charge 1.00-1.50 for gentle rides
Charge 2.00-3.00 for rides like the ghost train, etc
Charge 3.00-4.00 for small rollercoasters
Charge 4.50-6.00 for Big rollercoasters.

The key is to get, and keep, people in your park for these, so keep your park rating up (handimen FTW) cash machines easy to get to, and build at a moderate pace.  You need to constantly have new rides to get more people with pockets full of cash in.

Shops and Stalls help, but not too much.

Edit:

Oh, and regularly check how many people are one your rides and what people are thinking about them.  If no one is riding a ride and you get a lot of "I'm not paying that much to ride X", drop its price 20 or 30 cents and see if that gets people on it, keep doing this until people ride again.

Drowning the guests is a must.

ROFL who doesn't drown them:D

hmmm... memories :) I remember playing them all day and night back then. Especially RCT1.
But, as the Tycoon series is considered. For me, there's no better than Transport Tycoon Deluxe.

This was such a a fun game, but i haven't played it in a long time. I remember the first time my rollercoaster flew off the tracks and killed like 32 ppl. I was like O_O. lol

I used to love designing complete death traps and waiting for someone to ride it :-p

I remember for one of the challenges I had to have a certain amount of money (forget how much) a certain park rating, and 1000 customers in the park at a specific date. My cousin and I were doing it, and we were kicking @$$. 5-star park rating and WAY over the cash minimum! The final month begins, and we're almost at the 1000-guest number, (at about 950). about 3 weeks later, we're at 990. Last couple days were AGONIZING, as we had spent quite a bit of our cash to get the extra customers, so we had to spend wisely since we had no time to make it back. The number quite literally teetered between 999 and 1000 for the last few days (it didn't go to a single other number).

We failed.......




So, in happier news, does anyone know where I can DL this game now??XD

 I played the original, and expansion packs up to Deluxe, once they went 3D I lost interest in it.

Oh I loved those games.

Suicide coasters were so much fun.

Not legally ;)

I loved both the Roller Coaster Tycoon games. The third one will never count.