Who should submit ?

When our business gets a new customer, we recommend to them that they select a directory in DMOZ for a listing if they have not already done so and apply for inclusion. We also recommend things like Google and Yahoo Ads.

Who should be suggesting new sites into DMOZ, the web designer or the customer ? Do you have a preference ?

Should they choose a geographical or functional listing ? or both ?

It's up to you. Just remember, if you submit it for the customer and he knows your trying to get him listed in the ODP, make sure your customer knows that it could take a long time for his site to be reviewed depending upon how many sites are waiting to be reviewed for that category you submit to. I suggest you follow the guidelines as best as you can. The less an editor has to do to the site submission, the faster it gets accepted into the directory.

We don't care who suggests a site. Owner, designer or anyone totaly not related to the site, it is all fine for us. We only ask them to pick the one best category and provide a decent title and description.
If the site is of global interest you best pick a topical category. If the site is mostly of interest for vistitors in a limited area (and yes the usa is such a limited area just as any other country) my advice is to pick a regional category.