I don't think there is any particular concern with this being a "first double rifle" from the chambering standpoint. The 360No.2, however, should not be IMO.
Actually, I would encourage anyone to choose a BPE rifle as their first double. They are way less expensive than comparable nitro guns and for me, much more enjoyable.

Most importantly, your first double rifle should be one which you enjoy shooting and will give long service. The worst is that the gun is bought on the merits of the chambering itself and other problems or potential issues get overlooked.
Stock condition, bore condition, reliability of the locks, even the fit of the rifle can make an otherwise apparently perfect choice become a costly headache.
A double with wonderful bores in your favorite cartridge and wonderful metal condition is a total bummer with a cracked stock, especially if you're the one to crack it shooting hot loads!
I heard there was a Fraser double at the Colorado collector show that needed a restock. I didn't get to the show this year. Is the gun you are looking at a private sale or from a dealer?