I want to make a feat similar to Magic Initiate but with a few changes, but I'm having trouble going about creating Magic Initiate as the base using the homebrew.  I know that each Magic Initiate feat is separate for each class, but how would I go about creating the spell options that come along with the feat?

Do you mean like these?

https://www.dndbeyond.com/homebrew/feats?filter-name=Magic&filter-description=&filter-author=IamSposta&filter-author-previous=IamSposta&filter-author-symbol=102118565&filter-rating=-12

 Similar to those yes, but I cannot add them to my collection because I do not have a subscription, so I am trying to create something similar using the homebrew editor.

Okay. If you have the PHB from this website the easiest way is to make a feat using Magic Initiate (X)  as the template and then just altering it the way you want. Then just do the same thing for the others as well.

If you don’t have the PHB, the next easiest way is to buy the Magic Initiate feat from that book for I think $2 and then do it the same way.