(I received a Harry Potter grant a couple of weeks ago).
The grants so far have generally been timed with some sort of extra-site activity (release of HP7 Part II, release of the new 52, etc). The idea, I believe, is that we generate a lot of content around this topic when it may be of heightened interest externally. The catch here is that this really assumes that the grant will be consumed very quickly.
For example: I haven't had time to watch all the Potter films yet (hopefully over the next two weekends). I may or may not have questions as a result, and I'll certainly go over the questions again (I've already read them all with book-knowledge) before and after watching to see if I can add or improve answers. However, this will be 4-6 weeks after the release of HP7-2.
If generating content quickly is one of the goals (rather than a more long-term "let's get more experts on this topic" goal), then perhaps a criteria should be "expects to have the time to be able to consume the grant content quickly".
Although new questions is an interesting metric, I don't think it's the most important (and, if we do assume that there was already extra-site activity, then it may have nothing to do with the grant).
If a question arises naturally out of the grant, then that's great. If the grantee is stuck trying to think up X questions to ask to justify the grant, then I don't think that's great. We want interesting questions that don't have an easily found good answer elsewhere; those are hard to force. I enforce a personal limit of 2 answers per 1 question (2.39::1 at the moment) because I think the site needs questions from a wide range of people to be successful, and it doesn't really need lots more questions from me. So that means that I'm less likely to generate HP questions, even having got a grant.
I suspect there will be disagreement about this (and so perhaps I ought to have made it a separate answer). If there is agreement, then a useful criteria would be the number of questions on the topic already on the site that have no answer, or no good answers. I expect most grantees will go through the questions on the grant topic as they consume the grant and add/improve answers.
As I wrote elsewhere the grants so far (with the exception of the most recent) have been focused towards the highest-rep users (i.e. part of the purpose of the grant is rewarding building up the site to the nearly-out-of-beta status) - although most of the grants didn't reach their limits, so this was only partially the case.
Users that are right now rapidly increasing in rep are the users that probably right now have the energy and resources to translate a grant into site content. I think this is another reason that it's important to keep grant options open to these people.
Finally, although banners are out because some StackExchange users are a bit nuts I don't see any problem with having the featured tag applied to any current grant, assuming that there's only one at a time and it gets removed when the grant isn't available any more. If I understand correctly, this will place a link to the meta question prominently on the main site on most pages.