Finding a design Agency is a bit like finding a dance partner, ideally someone who knows the moves and won't step on your toes
Firstly don't delegate this task to a committee. They will complicate the process. It will take longer and ultimately cost more.
Start with a little research. Find examples of design you really admire. Then track down who produced it to create a shortlist.
Find out if any one on your shortlist is working for a competitor. If you are looking for a long term working relationship and think this may cause a conflict of interest, remove them from the list. If your project is a "one off " the chosen designer can always sign a non disclosure agreement.
Next, meet with the principle partners or creative Director of each organisation and ask them to show you their best work.
This meeting is vital to assess personal chemistry and define whether you will work well together.
Don't expect or ask for design ideas at this stage. None on your short list will have had sufficient time to understand the nature of your task. Anything visual they produce will only serve to complicate your quest. They should however, be able to express an opinion about how they would work with you.
Depending on your project brief, there are various ways you could agree remuneration:
1 Fixed fee
No matter how simple the project, a fixed fee arrangement should have a clear proposal of what has to be delivered and by when. Be particularly clear about expenses and outside costs like photography or prototyping which you might think are included but the designer does not.
2 Retained fee
This is useful if you have a regular supply of work and need to fix your costs for a year or more.
Designers welcome this too as it gives them a measure of stability and allows them to plan resources in advance. Bulk buy usually commands a discount but be realistic because your Agencies fixed costs will inevitably increase over time and this may be a factor to be reviewed at the mid point of the contract.
3 Fixed fee plus royalty
This is often useful to reduce the opportunity cost of developing a new product or in publishing. The designers however have to put their trust in your ability to get the product to market successfully so they can get the royalty payments. If you fail you will not get a second chance.
Try not to haggle over fees. Be fair and honest. Everyone has to make a living and the best deal is one where both parties feel happy and respected.
If you force someone to work for you on terms they find poor, you may never get them to produce their best work. Likewise if you feel you are not getting good value, make your feelings known immediately and find out why.