Most galleries and independent curators have a definite style or interest in specific types of artwork they are interested in, and it is a good idea to research this carefully to save time and money and avoid cutting off avenues of future opportunity. Many galleries have online archives of past shows which will give you a flavour of the kind of artist they show. If there’s a connection then engage with the curators work or galleries exhibition programme.
Recently there seems to be a trend in so-called galleries offering representation for monthly fees. Often young graduates are appraoched at their degree show or though their websites and it is not obviously clear at first that they wil be charging fees. Think very carefully if this a feasible option for you, having to pay both a fee and then commission on sales. Again research is useful, check their profile online, ask fellow artists if they have heard of the gallery/agents before you decide whether to accept their offer or not.
This site contains extensive listings of artist-led spaces, small and large crafts and visual arts venues as well as medium-specific venues which would make an excellent place to begin your own research.