I would like to hold weekly one-to-one meetings with my telesales team. What structure and questions deliver the best results?

First, I think it's a great move to have weekly, never miss one to ones. Daily meetings are too much and only meeting monthly or quarterly is not enough.

You should have a performace dashboard with each person. For telesales, I prefer the main metric being closed sales or qualified referrals to a senior sales person, depending on your business model.

Next, set up the meeting structure. There are four components. 1. what was accomplished last week. 2. what are the goals for next week. 3. what decisons or discussion items are there. 4. what are red flag issues that need to be brought to your attention.

Using a tool like Google docs is great because: 1. you can create a running list of meeting notes (great for reflection at performance review time). 2. the document is highly editable and auditable.

Require your direct reports to update the document by 5 pm the day before your scheduled meeting.

At a typical 1-on-1 you want to discuss opportunities (opps = i.e. deals your rep is working but has not yet won) and be able to both coach the rep and also forecast accurately so you have a good understanding of your business. Thus you will need to "inspect" those opps carefully. I would keep a Pipeline Review meeting separate from your Forecasting Meeting because those are slightly different but you can combine them for now. So focus on your forecasting objective and ask what I would call "3 Levels of Why" for each opportunity going beyond surface pain of your prospect's needs:
1. Identifying a specific pain that is quantified and implicated
2. Understanding a prospect’s goal for what they need to accomplish if they had your product. What happens if they don’t hit their goals?
3. Learning why timing is important. What happens to the prospect if they delay purchase?

This is sort of the classical BANT (Budget, Authority, Need, Timeline) but stronger because BANT is ordered incorrectly (should really be NABT or NATB depending on your sales process) and misses a C as in BANTC (Competition...against whom are you competing for the deal, even if "complacency" or doing nothing, that is still a C). Plus at different stages of your opportunity pipeline you need some but not all of the qualification criteria in BANT. At first stage of the buying process you really need to develop a rapport and understand the Pain (Need in BANT) so you don't need all BANTC at that time. To simplify - you need to know what stage the opportunity is in and ask the relevant question in that 1-on-1 meeting to ensure that the opp is in the right stage of the process and that your rep is doing all the right things to move it along. I'd start just with that in your first such meeting that you will roll out.

Separately, do you have a weekly "Team" meeting already too?

There are many types of such weekly team meetings - examples:
a) Weekly Monday morning pow-wow meeting
b) Weekly Pipeline Review with the team (i.e. this is not a forecasting one-on-one meeting but a group review of pipeline flow)
c) Weekly Film Reviews
etc.

So each one of these has a different purpose, structure and corresponding questions too.
I would make sure you have a Monday morning pow-wow and where you will also begin discussing Pipeline topics but this is a separate area that you should split out into a separate focused conversation some time down the road.

So at to get started on this meeting you may want to cover these three basic areas:
a) review key priorities from last week and make sure all goals were hit (i.e. # of Dials, # of Meetings/Appts, etc.);
b) cover key priorities for this week (i.e. product training with VP of Products, new spiff for prospects, a sales training session during lunch on Thursday, announce a newly hired sales rep, etc.)
c) and just as importantly, review your $ bookings metrics - where do you stand this week vs. where you should be at the time towards your monthly sales bookings goal (i.e. bookings trend) and give key guidance to the team on how to keep moving forward to hit the goal.