Should I transfer Domain host to GoDaddy?

I have my domain hosted by a 3rd party that uses GoDaddy, and it seems everything I try to do wants me to use GoDaddy. I went with another host because they were cheaper, but if it's going to cost a bunch of time and headache, I will transfer it. I tried to set up my email with G Suite and through my Office 365 account and both say I have to be using GoDaddy to get the email service to work. I called the host company, and they said I can use their email directly, and it's a cost savings, but am I going to have trouble with other things I try to do if I'm not using GoDaddy directly? Also, I am interested in the Affiliate program, but I don't know if I can participate if I am hosting my domain through a 3rd party.