I've never done this so I'm not sure, but here are some thoughts. If you want to use it for vocals and the guitar at the same time, you'll need an amp with a separate aux input, something like the Fender Mustang.
Mics often require phantom power and a preamp, and typically they have an XLR connector. Some guitar amps have XLR input, but I don't think it's that common. Using the mustang as an example again, the aux input is 1/8 inch You'll probably need a preamp with 1/8 inch or 1/4 inch outputs or a preampe with XLR output and an adaptor. This thing looks like it would work, but double check and adjust to your needs: https://www.ebay.com/itm/394675855391?hash=item5be483a01f:g:rIQAAOSwRQNkh0TU&amdata=enc%3AAQAIAAAA8BxcuD4xgd1reK3dnW%2Bk3BPNxKcXp06ZNoX2j3lwqx5nJboOso9lzio8vY65wyraZXTPtmFaf3rvP854syN%2FOiWcXaRU%2FkdYSParo7ZuceF1ex%2FMxafeQFX8MaQBcTkychsIchVuJSOii2PfLhtHABu6lRaRB6WhDKzleuF1KPwHxW3z%2BfuuPVub8XsIzd7brLmQs%2F41LUO7wsBNVgWVvFVtfGpUZ2KxLmOge%2FiiNfuykqGjtV8D14H9EvQYXyP0yh1YvdmlqtLvEFSlbkmgE4YS%2FscNAV2Joy7SKF%2FiOdKa04XsLRluPhA6k4RD9fJCUg%3D%3D%7Ctkp%3ABk9SR5zfzMeWYg.
I don't connect to a guitar amp, but I use the focusrite Scarlett 4i4 as an audio interface, and with adapters it might work. With something like that, you can also connect it to your computer for recording.
I've used an MXL 770, and for the price it sounds nice but you need to be close. It's more for talking than singing and I don't know if it's what you want.
You're going to need to consider feedback.
I'm no expert, so hopefully someone with more knowledge has better advice, but maybe this gets you somewhere.
Like this? https://youtu.be/p3PfKf0ndik