What kind of encodings are used for bypassing SQL filters? Does Hex or Base64 work? What other kinds of encodings are used for this? And if I'm trying to test the filter of a login function,
can I just put the encoded string into the input field, or do I need to use an intercepting proxy?
I know a proxy has to be used for things that aren't editable like cookies, http headers etc but do I need a proxy for things I can directly edit, like input fields?

Many encoding techniques won't work with SQLi since they will not be decoded and interpreted as SQL.

One advantage of using an intercepting proxy rather than just using a HTML form is that you capture a record of the HTTP request and response. This can be vey useful for going back and seeing what you did and tweaking requests. I've also seen sites that implement input sanitisation in JavaScript and avoing the web form also gets around this.