While there are many things that you may want for your podcast, there are two things that you absolutely must have: no limits and a valid RSS feed.
There is an absolute plethora of companies out there that will offer to host your podcast but very few of them actually understand the true nature of podcasting. A podcast host absolutely, positively must provide unlimited bandwidth, some mechanism so that you never have to take a show 'off the air' and a valid RSS feed for listeners to subscribe to. I recommend running, not walking, away from any podcast host that doesn't offer all three of these things.
Podcast files are not small by any standards. My weekly 45-minute podcast is 15MB or larger. Every time a listener downloads my show it takes 15MB of my bandwidth to do so. If your host limits the amount of bandwidth that you use then they are stating, in effect, that they are in the business of penalizing you for being successful.
The same applies to disk space. There are very few podcast hosts that offer unlimited diskspace, but this is essential. Consider my 15MB weekly show again. If my host caps my diskspace at, say, 150MB then that means I will only be able to store 10 shows at a time. When show number 11 rolls around, I will be faced with the tough decision of picking a show to take down so it will no longer be available.
Valid RSS Feed
Lastly, about half of your listeners will use some sort of podcatcher to grab your shows as you produce them. In order to do so, you need to provide a valid RSS feed for listeners to subscribe to. Without such a feed, half of your listeners are going to go somewhere else.
Your podcasting host is a partner in your show. It's great that you've gone to the trouble to make a show each week, but it's your host that makes that show available to your listeners. If your partner is limiting you in such a way that some of your shows might become unavailable to your listeners, then walk away.
You don't need partners like that.