So, how do we get from here:
to here?

It's actually a simple option! However, many people haven't noticed it, because it is somewhat difficult to find at first.

So, here's a not-so-in-depth tutorial.

Go to the "Game" button (as I call it). There it is! Options! Surprisingly, a lot of people click this button often to save/load/ragequit their game, yet never notice the options menu right there.

Resolution is near the end of the options list. Go ahead and turn it up, considering that the game recommends a Windows 95/98's processor... you shouldn't have any trouble.
NOTE: I understand that it says "Window" for resolution. By default it was 640x480 fullscreen, but PrintScreen wasn't working and I didn't have the patience to do this some other way, so I took my windowed image and cropped it.

Now, your game is fixed for full res!

Or, alternatively, you can click "Windowed" to give yourself a window that is, by default, 640x480, but easily scalable.

There is a glitch with this game where even if you are in Windowed mode, the game will only select things that are within the game window. Clicks outside of the window are not registered, even when you have already closed the game.

For me, the fix was simple: just spam left-click and right-click outside of the window until it works again. Hopefully, this will help.

Now here's a problem I haven't heard of with RCT yet, but have experienced with several other old games such as Age of Empires II and Populous: The Beginning, just to name a few. The infamous color bug is a result of Windows Vista/7/8's more modern graphics cards and drivers not being compatible with old games. http://aok.heavengames.com/blacksmith/showfile.php?fileid=11108
This is a link to a fansite for the game Age of Empires II from 2002, where somebody created a program for easily fixing these color bugs by running the program, selecting the screwed up game's exe file, and clicking Apply. After doing it once, you should never have this color issue again-- assuming you got it in the first place.

The download is in fact safe according to Norton, and while designed with Age of Empires II in mind, I've used it on many old games that GOG didn't even bother testing before selling, and it's worked almost every time. I wish Interstate '76 had worked, but you can only push your luck so far...

=UPDATE=
Okay, so there is another way to fix color issues. This has worked with Dark Forces II, the original Command and Conquer, both XCOM UFO Defense and TftD, and the original Age of Empires II disc.

Open up Task Manager using Ctrl-Shift-Esc after you launch the game. Go to the Processes tab and end Explorer.exe. After you're done playing, you can reopen Task Manager with that same shortcut and go to the top, where there's a "File" tab. Click "File" > "New Task (Run...)" and type in "explorer" without the quotes. Hit Enter and your desktop will reappear.

You may want to write down that Task Manager shortcut and the instructions if you don't know it entirely, so you don't forget it and get stuck on your blank desktop without a Start Menu.

As stated previously, Windows 7 and Vista can have problems with DirectDraw games where colors will show up horribly wrong. If you want to fix it yourself, one way to do this without downloading anything is to kill explorer.exe while playing. No, don't leave, hear me out!

Windows Explorer is the cause of the problem for Vista and 7. The pallete for these games get overwritten by the palette your desktop wants to use, and the result is a mess of colors that make no sense and are hard to look at. We can fix this with a simple BAT File:

First, you'll want to make a text document. After making the document, delete TXT and replace it with BAT. Yes, change the file extension, it won't become unusable.

For me, the path to the game EXE is this:
"C:\Program Files\Steam\steamapps\common\Rollercoaster Tycoon Deluxe\RCT.exe"
It'll be the path to where your Steam library is installed, then steamapps\common\Rollercoaster Tycoon Deluxe\RCT.exe. Don't forget those quotes, they ARE important to make sure the spaces are read as spaces instead of separate commands!

Once you make that BAT file, save it, put it in the RCT files next to the application, and make a desktop shortcut. The BAT will automatically close Explorer, open up Rollercoaster Tycoon, then re-open Windows Explorer as soon as you close the game. The only downside is that your desktop will disappear while playing and only reappears shortly after closing (or if you hit Windows+R and type explorer).

Here's an issue that's very uncommon. However, expect it to only happen once or twice after you've fixed it.

So, on the third time I launched this game, I exited to find my Steam window had been attempting to teach me about the time of CRT monitors and 8 bit color.

How do you fix this? It's pathetically easy. When you double-click the top part of a window, it will maximize itself to desktop size or go back to its normal window size. Double-click the top part of the window until the colors smooth out.

On some PCs, this will happen often while you're in game. Don't worry; while it might not fix itself while you're in game, it will either go away once you quit, or you can easily fix it after you're back on the desktop.

I was going to look for a solution for the game being unplayable on Windows 8 and 8.1.

Forget it, somebody already did.
http://steamproxy.net/sharedfiles/filedetails/?id=282196403

This guide should get you playing without a problem.

I had a problem with Battlefront II when I tried to play it at first. It would open up the menu and crash on a battle. I did my research, and it turned out to be a Sound Card issue.

How do you fix it? Go to your Control Panel. There should be a category called "Hardware and Sound." Once you open up this category, click the "Sound" category, and a little dialogue will pop up. Go to the Recording devices tab, right click some empty space on the dialogue, and click "Show disabled devices." One of the things that should show up is "Audio Mix." Enable it, and you're set for old Sound Cards. I've yet to have this affect anything else, so I just leave it like that.

Should you be having a problem you're not sure how to fix, you might as well try this one.

I think I've finally found the solution!

Just do the following:

1. Go to where Steam is located on program files > steamapps > common >RollerCoaster Tycoon Deluxe
2. Right-click RCT.exe and click "Properties"
3. Go to the "Compatibility" Tab
4. Check "Run as Administrator" and "Run in compatibility mode for..."
5. Set the drop-down menu to "Windows 98" or "Windows XP SP2." Can't remember which one, so just try both.

Here's something of interest for you PC gaming enthusiasts... it turns out a fair amount of people who have issues with old games have top-of-the-line graphics cards, like the GTX 980 and R9 290x.

It should be noted that GTX 900 series cards and certain R9 cards come with a form of supersampling called "Dynamic Super Resolution" (Virtual Super Resolution, for AMD cards). RCT isn't meant to go above 1024x768, so that's a bit of a problem. It is most likely the cause of the error where everything shows up in an unreadably small screen.

To fix this, right click your desktop and go to your graphics card control panel (Catalyst Control Center for AMD, Nvidia Control Panel for Nvidia). You'll need to make sure VSR and DSR are off for this game to work properly.

While you're at it, a driver update won't hurt. It's always best to be up to date with drivers, so you might as well make sure you've got the latest stable drivers.

If all else fails, try switching to your integrated graphics for this game. Don't worry, it runs on potatoes and you won't see any kind of performance impact. I think it's also worth mentioning that this particular step may be helpful in fixing many other old games.

EDIT: Enabling GPU Scaling seems to work as well. In AMD Crimson, you can go to the Display tab to find this. Not sure where it is in Nvidia Control Panel, sorry :(

Well, that should cover it.

So, now for a little present, for all you horrible people...
How's that for "Story or Lore?"

After 14 years of half-decent to mediocre sequels, hopefully this re-release will have been worth the weight.
Thanks, and have fun!