You've received some good answers, but this question has now been asked and answered a good half dozen times in the past week. Check out previous responses.

It depends on whether you are new or not.  At different stages in your career you need different types of support from a broker.

Nina Hollander nailed this one!

Mentorship abilities and Availability

What Nina Hollander said.

What is important to you? Make a list and talk to other agents in the firms you are considering. See what they like or don't like.

One with a good mentorship and/or training program. 

One who you can trust to help and be there within reason.

leadership, equal handed treatment of all agents, mentorship, understanding of marketing, appreciation of shifts, internet skills

If you are new to the industry, you would want someone who can support you and be available for you including weekends.

One that is approachable, available and can coach, nurture & guide

Chapter 15, Broker Selection

One who provides the services you need.

Interview them and look for right fit/match for your needs.  If you are new to the business, the proper training is critical.   Choose wisely.  

we are all cut from a variety of cloth.... what are YOU looking for... if I were newly licensed, I'd want training and mentoring....I'd need to learn how to market and make MY phone ring....

Broker number of closings and track record history

Broker kind and willing to train or has training of this century

Broker directs you to resources, kicks up your game,  expects the best you can be and communicates positive, clear and mindful goals.

What's important to you? Support, training, integrity?

Rebecca,

It is a mistake to give too much weight to the 'qualities of a broker.'

They ARE all engaged in the same business, and it is not the business new agents think. Don't believe a word they say. Choose based on the number.

What matters most is your COMMITMENT.

The first measure of your COMMITMENT is the preparation of a business plan. A business plan. Exactly what ANY business onwer would be REQUIRED to create. Without a plan you give the broker NOTHING to work with therefore they make no commitment on which you can rely or they need to deliver.

Your business plan equips you to measure the broker, not the broker assess you.

Next, can you follow instructions. A plan and willingness to be taught are required of you. Of the broker only one measure applies.

(#agent/#ann Transaction => 2xNat aver)

Their commitment is to engage you in your preferred transaction type (spelled out in business plan) within 30 days. You learn by doing, NOT warming a stool in a conference room.

Find that broker and simply follow the instructions of the mentor assigned.

Coach, mentor , friend, boss

Rebecca Jewkes One with good rapport and who has a good mentoring and training program.

The right chemistry and support tools!

A broker who is available and able to teach

Others have answered.

Their reputation, an agent support, knowledge and experience. 

He or she should be a good manager and a good listener.

Remember, you are interviewing THEM, not the other way around, Rebecca Jewkes!  And, you've gotten some great answers as to what YOU are looking for when you select one!

One that will best meet your personal needs.