Actually, most cable modem connections are more than good enough to self-host a MUD until it gets a regular population of 20+ players. The only caveat is that you have to impose a little restraint when using your connection to download things (or setup a bandwidth limiter).
Seriously guys, a MUD take almost no bandwidth, and as long as your link is not saturated, latency is also not an issue.
There are good reasons to host with a real service provider (I would suggest a generic VPS, not a MUD specific one unless it's free.... the price different is tiny and a full VPS gives you far more control). Those reasons tend to only come into play when you have a stable playerbase. Certainly there's no reason to worry about it when you're still developing.
With dynamic DNS updates, even if your IP address changes (mine does about twice a year), it's not likely to cause many issues. While you may have slightly more downtime than you'd like... unless you're paying good money, I'm not convinced a "professional" service will be better. Ask them if they guarentee 5 nines of uptime? I'd be surprised if they guarentee ANY amount of uptime unless you're shelling out several hundred a month.