You just opened up a can of worms.
Couple options.
I use a small chestpack from fishpond, the san juan. To give an idea what it fits I can take two fly boxes on the inside, or one on the inside with my other material like random spools (dont fit the brand i have most of), and some other things like my license and phone in an inner zip pocket.
now I also have a ton of flies on a drop down bench that i meed to re-organize as I have gotten lazy when changing.
Now one of the best things you can do is maximize the space on the out of the vest. I carry 5 tippet spools on an external tender, forceps, nippers on a zinger, a fishpond trash can, and also a leader straightener on a zinger (I may or may not keep that on though).
Now I love my chestpack when I know I can take one or two fly boxes and be good for the day. It is small though so spare spools (if needed) often wind up in my wader pocket.
I like a vest for when im carrying 3+ boxes, spare spools, replacement stinger hooks, fertain floatant bottles etc. The vest also has a rear pocket for water, a jacket etc.
Vest styles are vastly different. Mine is a no name mesh vest from 10 years ago, and is more traditional in its design.
If I was to get a new one I'd be looking at Simms, Fishpond, or William Joseph. Personally the William Joseph Exodus is an interesting pack, as it has an integrated backpack but can be removed from the vest portion, leaving you with a chestpack/vest hybrid. I recently got to look at one as my dad ordered it, however at $200 or so it isn't cheap.
Whats your budget?