OK...~400GB, going into a 500GB SSD.
That will work.
Any of the current cloning tools will do this. Acronis Trueimage, Macrium Reflect, Casper, Easus Todo, Samsung Data Migration (if you have a Samsung drive).
So....
Install one of the above applications
Disconnect all drives except the old HDD and the new SSD
Run that application, and do whatever it says
Hopefully, it actually works
Power off, and disconnect everything except the new SSD
See if it boots correctly.
If so, then you're golden. Wipe the old HDD
As far as new applications and games? You can install them on whichever drive you choose.
During the install, select Custom or Advanced. This gices you the option of 'where'. Also, you should do this always anyways. You can prevent many applications from installing their included junkware.
Steam games? Directly in the Steam client, you can designate other folders and drives to install to.