There are many considerations to take into account when choosing a lawyer.
Price is certainly one consideration, but should only be one of many. For instance, if a lawyer is quoting you a very high fee, is s/he worth the extra amount as compared to another attorney who may have slightly less overall experience - but who's intellect and diligence level compares favorably to the more expensive attorney.
There are also attorneys out there who charge very low fees or charge clients a fixed fee only when they appear in court. A potential client should consider whether the attorney charging such fees is very inexperienced compared to other attorneys, or is "running a mill" - in other words, has a caseload so high (100+) that there's little chance s/he can devote quality time to your case. There have been studies done which say family law attorneys should not have more than about 70 cases at a time. Thus, ask your attorney how many cases the have - if s/he doesn't know or can't answer that question, good chance the caseload is so high s/he lost count.
Then there are attorneys who charge a fixed fee when they show up (say $500-750 per court date). Here's the problem: if a lawyer makes his/her money only by showing up to court, what's the incentive to actually prepare for court? Obviously preparation depends on the complexity of the case, but I often tell potential clients that for contested custody or divorce cases, I often spend at least 1 out-of-court hour for every in-court hour (sometimes far more than that). Thus, unless your case is extremely simply (and if its in-court already, then it probably isn't), then having a lawyer charge you a fixed-fee is probably doing little more than ensuring you have a warm body next to you in court.
Next consideration is experience. On the surface, one can say having a lawyer with 30 years experience is better than having a lawyer with 10 years experience. And while as a very general rule that's true (wisdom does count for something, after all), it is also good to get beneath the surface. For instance, if one lawyer has 30 years experience, but only devotes 40% or less of his/her practice to divorce/family law, and another lawyer has only 15 years experience but devotes 100% of his/her practice to divorce/family law, then one can make a good argument that the latter has more relevant experience than the former.
Furthermore, what is the experience? For instance, perhaps an attorney who has 25-30 years experience currently devotes the majority of his/her practice to divorce/family law - but has it always been that way? In other words, the attorney can say "2/3's of my cases are divorce/family law cases." But the attorney could have shifted his/her practice areas just in the last few years (for example, having done mostly property transactions or estate work up until recently).
Moreover, if your case involves contested custody issues, ask how many custody cases the attorney has actually handled. Many potential clients are not aware that some family law attorneys concentrate in doing mostly divorce cases (and thus very few family court cases), or most family court cases (thus doing very few divorce cases). It is often best to have an attorney who has experience, but more importantly relevant experience to your case.
Likewise, if your case looks like is may result in a trial, ask how much trial experience the attorney has. Some attorneys in the family law field concentrate on out-of-court settlements and thus shy away from heavy litigation. If one attorney was a former D.A. or prosecutor & thus handled numerous trials versus another who sat in a cubicle in the many years after law school watching the senior partner going off to court, then that's something you should know about.
One factor potential clients may wish to ask about is what law school the attorney attended as well as his/her graduation rank. For example, if an attorney graduated from a poorly-ranked law school (rankings can be verified on U.S. News & World Report - but be sure to look at where the school was ranked when the attorney actually attended the school) that may be one factor considered. Also, if an attorney graduated at the bottom of his/her class, again this is something to factor into the overall analysis.
One can ask: how on earth is law school stuff relevant anymore for an attorney who graduated 25+ years ago? The way I look at it, if s/he graduated towards the bottom of his/her class, this may be indicative of laziness or lack of (relative) intellect. While it's certainly possible things have improved with age, my gut says "old habits die hard" and such factors should be considered (even if they are given less weight than other factors).
Finally, how is the initial consultation dealt with. Does the attorney seem too busy to give your case adequate attention? Does the attorney seem friendly or unfriendly? Did the attorney just charge you for the pleasure of meeting with him/her for the first time (think about how many other businesses actually charge their customers before they provide any service). Establishing a good connection with your attorney is important as you must see this as forming a relationship, not just signing a contract.
While there are other factors which may be taken into consideration, asking the questions outlined herein will certainly get you off to a great start.