Installing the mod that bypasses the disc and running the game in compatibility mode for Windows XP SP2 fixed the problem for me. A modified Sims.exe to do this can be found here:
I have uploaded it to Google Drive, as the website I found it on was a bit sketchy. I scanned it with my anitvirus and it came up normal... Google Drive also scans anything you upload with it's antivirus, but regardless use at your own risk. Please note that this is not a link to a pirated version of the game, just a fixed Sims.exe that will allow the game to launch on Windows 10. I own the game and installed it on my computer via the installation disks. Obviously you will have to own the game too for this to work.
Instructions on getting it working:
1.) Make sure you already have the game installed on your computer.
2.) Go to :C > Program Files (x86) > Maxis > Sims. Rename the Sims.exe to sims.old. Make sure you keep this file in case the new one doesn't work.
3.) Download the file and move the new Sims.exe to the same folder (:C > Program Files (x86) > Maxis > Sims).
4.) Launch, run the game in compatibility mode if necessary.
5.) If it works, enjoy. If not, remove the new Sims.exe and change the old one to it's original name.
Good luck.
Hopefully this helps anyone who's spent hours searching the internet trying to find a solution to this issue.
All credit goes to this simmer here. It worked for me, I had each game installed up to making magic. I had to click on cancel everytime it told me to laod the disk the first few times but now my game loads no problem.
Just a reminder if you don't play the game in full screen you will have the black box issue and it can easily be resolved by just pressing the control, alt and delete buttons and just exiting out of that screen. Once you back to the sims screen the black box will be gone

Just like I showed other simmers here
I do the black screen everytime I load it, all you do is hit the
control alt and delete key and then cancel the page then its back to normal

So game loads with just a black square

Hit the control alt and delete buttons

That screen will come up, it has cancel at the bottom, just hit the cancel button. I can't printscreen that page so had to look for this one on the internet via google image
When the above page exits your game will be perfect minus the black block
This only happens if I play my game in minimised windows, when I was playing it in full screen it did not happen one time, game ran perfectly, I just prefer minimised screen 
I hope this helps some of you to play on windows 10
Comments
Its a pleasure
I don't exactly know what you mean, but I found this guide on how to install sims 1 cc
http://www.thesimsresource.com/helpcenter/view-post/post/23072/Installing The Sims 1 Downloads
https://www.facebook.com/EugeineZaneNelMissingperson/
Yay glad you came right, post lots of pics of your gameplay
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what do you mean by this? do i need to download windows xp sp2?
also i tried to put the new sims.exe file in the sims folder but i got "fatal error, could not find the sims data directory"
When you say 'rename the old one just in case it doesn't work' - what alternatives do we have if the file doesn't work? is it because this is for all expansion packs and I just have the deluxe edition? I'm not sure what other alternatives I have to get this game running on Windows 10.
Edit: It worked! Thank you!
I no longer have sims 1,2 and 3 on my laptop since sims 4 became bigger I uninstalled it. So unfortuanatly I can't help you sorry.
If I remember correctly, I am sorry this is a while ago now, the file mentioned is for sims making magic, so you will need to have that one with your deluxe to let it work sorry.
I could also only play 800x600 but then I did a thing in the properties that allowed me to play full screen. I think I had to add a -w at the end of the target in properties. I will try and find that for you, since I found it online for myself.
https://www.facebook.com/EugeineZaneNelMissingperson/
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I did not have any problems with the game itself, but it turned out my laptop was not windows 10 compatable so I had to revert back to windows 7. Doing that I lost everything so I never reinstalled the others, only 4
https://www.facebook.com/EugeineZaneNelMissingperson/
@mcrudd
I was looking for exactly this piece of information.
Thank you very much for sharing this advice back in 2015
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Windows 10