I am creating a Hombrew campaign that will not have any caster classes. Alternatively when i have the players make a character they get to choose either INT, WIS or CHA as their spell modifier and will have access to certain spells as they level up. For example is  a player chooses INT they will gain access to wizard spells. At level one they will; be able to choose 2 cantrips and a level 1 spell that they can cast 2 times per long rest. At later levels they will gain access to higher level spells and additional uses. 

This is my first time attempting to homebrew anything on DND beyond and am having difficulty. I was able to get the option to choose one cantrip, but not a second at lvl 1 and a lvl one spell. but was unsuccessful adding the options for higher levels. Example at lvl 3 they will gain a lvl 2 spell. Is it possible to make a variant race that has these kind of options? Or will i need to make a Class or subclass that will include spell casting? 

Any help would be greatly appreciated.