It just depends on your uptime requirements. Most non-static IPs from providers don't actually change that often. But when it does and you have to update your DNS record, it may take a day or until certain providers refresh their cache, even if the TTL is set low (lots of providers will just ignore TTL).
I recommend you just get a vps or shared hosting myself. Besides your IP changing, you could have disk problems, power issues, etc. There are different things that cause stuff to go down, a vps / shared hosting provider should be more prepared for these.
Also, depending on your agreement with your provider, you might likely be in violation of that agreement by hosting something (Though that doesn't often really matter).