Almost all projects (except for very simple tasks), involve a number of stages which the writer will need to work through. An experienced writer is able to anticipate these accurately when he or she considers the job, and the quote will reflect time for these.
Look out for this! If a writer can't plausibly itemise the stages they're going to need to go through when quoting, it's a sign of inexperience and suggests that they may not really understand what your job entails, which will mean you'll struggle to get the job done to your expectations by that writer.
Aside from anything else, because an inexperienced writer will often not allow in his quote for much of the work that will be required, he will later find that time for which he has not agreed payment is being consumed. This rarely leads to trouble-free delivery of a high quality job.

Check your copywriter genuinely has the capacity, at the time, to take on your job.

As in many freelance occupations, most copywriters experience busy times, and quieter times. This makes writers reluctant, during busy times, to turn away projects. There are only so many hours in each day, however, and a backlog can soon build up. If you're offering your project to a writer, make certain he or she has worked out the number of days that will be required, and that they are able to tell you precisely when these days can be scheduled into their workload. Remember that good writers tend to be busy. You should question carefully anyone who claims to be free to start a lengthy project immediately.

Think about whether your copywriter has the experience and breadth to properly understand the subject matter and context of your project.

As in all things, the experience of the suppliers in the copywriting market varies greatly. There are some excellent copywriters available who lack experience, but have a great deal of talent, and for some projects such a writer may well be an acceptable choice. For other projects, however, such a writer's inability to properly grasp the subject about which he or she is writing, or to really understand how the matter in hand fits within the broader context of, for example, your sector, may prove frustrating for you and, in the end, impair the writer's ability to complete the job to your satisfaction.

Does he or she have the commercial experience to appreciate your business objectives?

There are aspects of many projects which call on a copywriter to have a good general understanding and perspective on business and commerce. These are not, unfortunately, easy qualifications to acquire. A writer who lacks them, however, may have difficulty in helping you gain maximum commercial benefit from whatever item it is he or she is writing for you.

Look for professional experience. A good copywriter will be able to ask you probing questions and, later, to fill in the gaps in what you say.

A good copywriter will ask you questions about your project, its objectives, timings, audience and myriad other things. The less detailed you are in your prepared briefing, the more a good writer will ask. Equally, you'll find a good writer feeding back to you things that you've omitted to mention, or sometimes even to think about, but which his or her experience suggests require consideration. You should be aware that if a writer does not ask questions in this way it doesn't mean there are none: it means only that he or she lacks the experience to foresee them.

Ask your copywriter for a fixed first-draft date.

You want to see the first draft of your copy within the timeframe the writer agrees with you. This draft may well have all sorts of issues still to be resolved, and that's fine, but your writer should be able to get this document into your hands by the date agreed. There are, curiously, writers who never actually manage to complete a draft. I know this because, every couple of months, I'll get asked to take over such a job.