Welcome to the dark side Equiniphile!
To go along with what Strange has said - I highly recommend HACKING!! :)
Hack, hack, hack, hack, hack, and hack some more. Then, when you are done hacking, add some more hacking onto the hacking you've already done.
You can never do enough! I cannot emphasize that enough. You need the conditioning to beable to cover all 3 phases *in most cases in 1 day* and to beable to cover a CC course. You may be surprised, you may think the both of you are in shape, but when you are out on a CC course in a comp, you think...sheesh...is this over yet? Lol.
CC courses are very demanding, even for BN - so conditioning is very important. You want to condition your horse physically - but also the importancies of this factor, are the heart and the lungs. Strengthening the heart and the lungs are very important. There are lot of great articles in the Practicle Horseman Magazine Archives you can dig up online, that'll give you great advice - articles written by "greats" including Jim Wofford, David O'Connor, Becky Holder and others. Very benefitial reads.
During my Eventing Season *cause that's all I do* I hack as much as I can. Get on hills, get on those trails, terrain and condition your little heart out. Work on a functional 2 point while out there, condition and strengthen your legs, your core, your upper body, your lungs. Work on staying off of his back as much as possible to get your body in shape, and all the while, working on your horses conditioning as well.
When I am out hacking, I work on intervals. Walk, to trot, to walk, to trot and gradually increase by adding canter work in there. Working on getting his back lifted and up into my seat, engaged, off of my hands *meaning on his back end and carrying himself*. And then other rides I just let him be and focus on me.
There are so many things you can accomplish while out hacking - I say stay off of flat land. Flat land is ok if you are just starting out, and just getting back into a conditoning program after having a lot of time off - but if you have uneven terrain, all the better - because guess what....your CC courses are rarely ever flat...even for BN courses.
I hack most of my time during the week, and I get in the arena once or twice a week. I have a lesson once a week, and my Coach is an Eventer *competes Prelim* is very competant in working on Dressage with me, and Jumping. She is very involved in the sport, who's coach is also very involed (She is 3*) and her Coach is far above her in the sport...etc, etc - the education trickles down - so I am happy to not have to have 3 different coaches.
I also Clinic as much as I can - I do more Clinics in a season than I do comps. The more you learn, the better - especially in this sport, due to it being one of the most dangerous equestrian sports out there.
While I agree that dressage is of the utmost importance, a lot of times it can be quite a lot for a younger horse mentally, and I've always found that jumping is a bit of a mental break sometimes, especially since you probably won't be doing anything incredibly difficult with him quite yet. I suggest trailering him out to the other barn, or possibly seeing if that trainer would be willing to travel to you once a week, and you can travel to that farm once a week, a bit of a compromise I suppose.
You are right - dressage now, has become the most important phase in Eventing, due to the new formats that have become a huge part of Eventing as we know it today. *I want the old formats back*
But, while working with a "Greenie" you do not always have to do dressage in an arena - you can do this while out hacking. Working on bending off of your leg, becoming light to the riders aids, working on smooth and fluid transitions and etc, etc, etc.
Hacking is very benefitial :) But I agree, GAG and BN wont be too difficult. Just basic "Training Level" dressage.
I also agree, hauling to a coach once a week will be very helpful at this point in time!
All the best Equiniphile, let us know how it goes!