Lawyers get into the act as legal advisers to the parties or mediators. When the stakes are high, you may want a lawyer at your side. At least, consult with one before you sign the final agreement. Mediators are unlicensed so their training and experience can vary widely. Facilitators often have counseling backgrounds.
Evaluators tend to be lawyers.
The choice is a matter of preference. Either way, make sure the mediator knows your field if you have a technical dispute, such as one dealing with construction practices. The key to effective mediation is timing, says Lovenheim. Disputes are ripe for mediation when parties understand the case against them and their options, but aren't frozen in their positions. Start mediation too soon and neither party will have a clear understanding of its interests.