Could you have a cage of 1,550 square inches or more?If so,a Syrian could work really well
Around 40 inches x 40 inches is one example of that cage size,while a dwarf could have something half the size and mice could have even smaller.
You might find that if you end up deciding on just one you'll end up eventually wanting both.That's only a problem if you can't fit appropriate cages for both and can't afford proper care for both,but to be honest mouse cages are very easy to make space for.
DIY cages are definitely cheap in the US.Home Depot sell melamine sheets which are 4 feet x 8 feet,which can make one cage or several cages depending on what you want to house and what other materials you use along with the melamine.That single sheet only costs around 30-35 dollars,and if you're making several cages with it it can be an absolute bargain.Plexiglass is a good option as well,but it can become expensive unless you can cut very large sheets.You could get about 4 4 ft long x 2 ft high sheets out of a single 4 x 8 plexiglass sheet though,so if you build two Syrian cages with front and back plexiglass panels that actually covers both cages.So,you initially pay up to 200 dollars for materials,but end up spending far less than a smaller premade storebought cage would cost.You might even spend 150 dollars or less on materials,and if you make a Syrian cage but only use one plexiglass panel you could even make cages for many other animals as well!