First, congrats on wanting to keep your grandad's legacy going - well done indeed.
Nice plane! Your plan to restore her is a good idea - and what I see in the pic shows it's actually pretty much well along the way. Mainly, the
basics to finishing her are engine/motor (fuel/electric - and I recommend electric today), radio & connections (to control her) and the paints necessary to finish her and make her look nice. Finishing her yourself really isn't all that hard. If you've got any experience at all with woodworking, you already have the basic skills. If not, you might actually consider getting an inexpensive stick-kit like this pic:
(Herr Engineering Piper Tri-pacer - sold by
SIG Mfg Co) and finishing it to static display status just for practice. If you can build this plane, you can finish your grandfathers plane - the structures are quite similar.
Before anything though, I'd suggest looking up one of your local
Academy of
Model
Aeronautics flying clubs and talking to the guys. They're close to you (2 in your area
WITH trainer personnel - PM coming) and you'll get the best advice possible from them. You'll also have the advantage of one-on-one interaction with a lot of experience. One of the first things they'll probably tell you is to get a basic trainer aircraft to learn to fly with - your grandfather's plane is NO KIND OF TRAINER, it looks like it might be a scale model in the pic, and you'll want to know what you're doing before you take her into the air. They'll probably also recommend joining AMA so you can learn to fly with them. Reason for that requirement is insurance, mainly. Model planes, while quite reliable, CAN cause havoc - actually, it's usually the pilot that causes the havoc with the plane. Anyway, membership and the insurance IS a good idea and you should seriously consider it.
There are tons of things to learn - don't get too overwhelmed in the process. Take your time, get it right. The clubs can/will make it fairly easy, and a lot less daunting. Cost: yeah, it's not cheap. But, if you spread the costs over a reasonable length of time it'll be a lot easier to manage. You don't have to go and buy everything at once. I'm not going to throw any kind of number at you here - way too many variables in the mix. I WILL say you're looking at several hundred $$ though. Spread it over a year or so. No rush in any of this.
One other item - and I'm speaking as a grandfather here; you've already demonstrated your closeness to your grandfather. While you definitely COULD find someone in the local club to rebuild/finish the plane, you're going to find a HUGE satisfaction and self-reward by doing it yourself, with help. It'll surely tighten the bond you had with him, and you're very likely to find yourself becoming as much a fan of airplanes as he was - AND THAT'S A GOOD THING!!
I've mentioned a few of the basics. I'm hoping a fair number of others will pop in here to add to it. The more you can absorb, the better your experience will be.