First: there's a lot of marketing fluff involved in the 'C' rating of a battery.  So read the label carefully, and if it bursts into flame any way just don't buy that brand any more.

Second: You're probably OK with today's batteries, unless you want really short flights on light batteries.

The 'C' rating of a battery is an estimate of the amount of current it'll generate, as a proportion of its capacity.  So a 1000mAh, 1C battery, should be used where its not going to deliver more than 1 amp (1A = 1000mA).

You want flights that last about six minutes (I assume), which means that you want a 10C or better battery (in theory running the battery at 10C would bring it to 100% discharge in six minutes -- but remember that you're aiming for 75% discharge or less, so 10C gives you some overhead).  If you're desperate for weight savings and you don't mind using the batteries hard you may want to do something like plan on a three minute flight with 20C batteries.

I don't necessarily trust numbers over 15C, unless the battery manufacturer is one of the known-dependable 'big names'.  Because there's no standard for what the 'C' rating for a battery is, rating a 1000mAh battery as "30C" could mean anything from "pull 30A for it for one second and it won't burst into flame but all other warranties are void" to "pull 30A from it for 90 seconds every day for a year and then think about replacing it".  It really boils down to how responsible the manufacturer is about trying to sell batteries to not disappoint vs. selling them to make money quick.

So -- how long of flights are you planning on?

I bought some batteries from Hobby King and so far they're OK -- but I've been using them in RC planes at less than 10C rates.

If you're really going to fly for just three minutes and you want to keep the batteries light I'd say look for batteries that are advertised at 20C or better, and if they say "continuous" that's even better yet.

To some extent the motor & battery you get depends on the airframe; make sure you have an idea of the all-up weight of the airframe is going to be before you get the electric stuff.

Good luck with your mom, and my sympathy -- having one of my elder relatives succumb to Alzheimer's is something that I dread.