Aside from start early (specially if you want customized rings), setting a budget, here are some other tips that if you think about it, really make sense. I listed them down according to level of importance (at least in my opinion).
Consider Form and Function
Your ring should respect your lifestyle: Those who enjoy sports or music should opt for a slimmer ring with rounded edges (appropriately called a "comfort fit"), rather than a wide, bulky band. Those who work with their hands will want a simple, solid metal ring, as stones can come loose and carvings will trap dirt. And those who are highly allergic to certain metal alloys will want to invest in platinum, as its purity renders it hypoallergenic for most people.