There are two parts to your question. I will answer the second one first.
Remote hiring isn't as remote as it once was. After rule in age of telephones, Skype, and FaceTime, you can spend a lot of time with someone evaluating them even though they may be in another city.
As for best practices, the most important practice to be established is determining what it is you really need to hire to be satisfied with your new employee. Remember, every criteria you add to the mix reduces your pool of potential solutions to your problems.
Once you have a clear idea of what you really need, you need to figure out how you will assess for that experience. If you were going to ask other people to interview a candidate, you need to get them clear on what they are to interview about, and what they need to assess for.
Too often, colleagues take job hunters down rabbit holes that they don't deserve to be taken down. Everyone in your organization has to be clear about what they are part of the assessment process his head what they are to interview for otherwise you will turn off way too many people.
Tip of my hat to Jeff's answer.
I will add my perspective in more of a 'big picture' way.
The biggest frustration people have in hiring - be it local, regional or international - is getting it 'right'.
'Right' is defined as the right person, at the right time, for the right job.
So in other words, whatever question(s) you ask, each must lead back to this Right Fit principle.
A caveat is to be prepared that you, for whatever reason, do not find the 'perfect' candidate (if there is such a thing).
What will you do then?
Line out your wants, must-have's and wish list of attributes. Make these clear to applicants for it to be fair play.
Last thought - know that introverts may 'bomb' the interview because of the communication situation, and not because of their worthiness. Use both written and verbal responses to judge best candidate.
Let's get on a call and get you the right hire!