Here are some factors to consider, often times the church sells you a package that includes the minister, priest or rabbi to conduct the ceremony. This can often include the church pianist or organist, for traditional weddings it might work well for many brides to go with the musician offered in the package. In some cases the bride might have always dreamed of having a string group perform "Pachelbel's Canon" for her Bridal March, in which case she could opt to have a string trio or quartet play all the music for the seating, ceremony and recessional.
Another option is to have the pianist/organist provide accompaniment for a solo violinist or flutist etc., this can be a great option for the budget conscious! If you always dreamed of having a harpist play at your wedding ceremony, they will certainly like the easy load in (more later about that) and the good acoustics of most churches will compliment the harp. Be prepared to spend a bit more for this option.
As a wedding ceremony musician myself I can tell you that when Mother Nature cooperates there are few things as memorable as getting married on a beautiful beach around sunset! Most venues have a Plan B when Mother Nature is not in a good mood, but let's assume the best, that it's a beautiful day on your wedding day! Unlike the controlled atmosphere of a church or temple, when you are on the beach with a peaceful breeze blowing, possibly others walking by who are not in the ceremony you may need to put a microphone on your officiant in order for your guests to hear the ceremony. This is true especially when you have more than 30 or 40 people on your guest list. I mention this because often your musician can often supply a wireless mic for the officiant and bring a small PA system for a modest extra charge. Obviously having power outlets available can be an issue unless they are using a battery-operated system. With that out of the way let's concentrate on what makes a great beach wedding when it comes to music. First of all if you want the laid-back island feel a steel drum player can provide a nice atmosphere, they can often play cheerful Calypso music for your guests to be seated by. Then they will play your choice of music for the wedding party and then the Wedding March or whatever you've chosen to walk down the aisle to. For a modern, hip wedding you can also go with an acoustic guitar player, the steel strings tend to stay in tune better on a warm beach day and many young couples prefer to have some modern music in their ceremony these days.
It is also possible to have string groups play on the beach, although miking them can be an issue for a larger group of guests to hear them well, especially on a windy day and that goes for the officiant as well! A small foam wind screen over the microphones can help when the breeze is light to medium strength, but when it is blowing hard it is all but impossible to get rid of that wind noise over the speakers! Usually a large dynamic mic with a windscreen does a better job than the smaller lavalier microphones that clip on to the lapel. Other combinations that are nice on the beach include guitar and violin, or guitar and flute as well.
Garden Wedding ...or nice backyard : )
Our last category is similar to the beach wedding due to being outdoor and susceptible to wind and other whims of Mother Nature. The same advice regarding microphones is applicable as well. One more thing to note is that pretty fake columns, flower holders and other decorations should be anchored securely in case the wind picks up and they fall over in the middle of a ceremony! ...true story for another time
If your dream of having a harpist is to come true remember that most harpists insist on having a flat surface like cement to roll their 7 foot high harps on and then ultimately set up and perform on. The harp can be amplified for larger crowds, some have a microphone built in that works well providing there is a PA system with the necessary power. Guitarists are also great and having them sing and play for ceremonies is becoming increasingly popular. Songs like "Marry Me" by Train or "I'm Yours" by Jason Mraz are perfect choices.
Where do you find your musician once you decide what you want? Many pros have websites with examples of their music, keep in mind that video examples are always better than audio mp3's to hear what they will really sound like live at your wedding. Hiring a musician is the same as buying any other product or service, be sure to check Google for reviews and referrals from their previous clients are worthwhile as well.
With all the information above I'm confident you can move forward in choosing the right musician to play your wedding ceremony that will fit your theme, budget and tastes! Next you need to choose the music for them to play but that is a topic for another day! Good Luck!