First off, thank you for making this thread and asking for our opinions - the community really appreciates it! I almost exclusively play Halo BTB, so I feel pretty strongly about keeping it a permanent playlist. My thoughts on what you said you're curious about are below (apologies in advance if it gets too lengthy):
1. Starting Weapons
I personally prefer using the Stabilization Jets BR or Long-Barrel BR as opposed to the default version, but wouldn't be too upset if the default version was left in. I'd strongly prefer ANY type of BR over the magnum, which I think should be reserved for 4v4 Arena gameplay. The AR is an appropriate secondary weapon in my opinion.
2. Vehicle Gameplay
I love vehicle gameplay, and think it's an integral part of the Halo BTB experience. But to be honest, I've been pretty disappointed with the Halo 5 BTB vehicle gameplay. It saddens me to see how the Warthog has been reduced to a utility vehicle that's only used to pick up the flag/bomb carrier, and rarely utilized to help control the map (except the Gauss on Viking). It's far too easy to shoot the gunner out, and just isn't viable on most maps. The only maps in the current rotation where I think the Hog is really effective is the Gauss on Viking (which is extremely effective and fun) and the Chain Hog on Scavenger. One way to increase the usefulness of the Hog would be to reduce bullet magnetism on the gunner (similar to the current mechanics of the Mongoose).
It also feels like the current BTB rotation is a little too vehicle-light. Eagle Square, Traffic Jam, Port Authority, Boulevards, Deadlock, Scavenger - none of these maps have any heavy vehicles. I personally really enjoy Port Authority, Deadlock, and Scavenger, but at times it feels like I'll play BTB for hours at a time and not be able to use a single heavy vehicle. At times, the current version of BTB feels more like regular Team Slayer...only with 8v8 crammed in instead of 4v4. I think the lack of vehicles in regular BTB is a big reason a lot of players (especially less experienced/more casual players who don't just want to use a BR all day) prefer BTB Super Fiesta, which has tons of fun vehicles to use. A good mix of more vehicle-based maps (i.e. Viking, Dispelled) and more infantry-based maps (i.e. Deadlock, Scavenger) is key to a good BTB experience.
For example, Traffic Jam in particular feels stuffy and cramped for 16 players (Traffic JAM is a fitting name). Think of the most popular BTB maps in each Halo game. Halo CE - Blood Gulch; Halo 2 - literally EVERY map had vehicles (Coagulation, Terminal, Headlong, etc.); Halo 3 - Sand Trap, Valhalla, Avalanche; Halo Reach - Hemorrhage, Paradiso, Boneyard, Spire; Halo 4 - Exile, Ragnarok, Vortex, Longbow; Halo 5 - Viking. These are all big, open maps with lots of room to move around, plenty of power weapons, and at least one heavy vehicle. Small maps like Traffic Jam don't stack up to any of these, and simply don't feel like a classic BTB experience.
One thing I'd ask is to please continue to make sure that all vehicles are represented in the new rotation (i.e. ensure there is at least one map with a Scorpion, one map with a Banshee, etc.). I know people complain about Dispelled a lot (and rightfully so, because it can become lopsided very quickly), but without that map there wouldn't be a single map in Arena where you'd be able to use the Scorpion, one of the most iconic vehicles in the Halo franchise.
3. Mode Preferences
Keep all current game modes represented (Slayer, CTF, Assault, Strongholds). The variety of game types keeps things interesting and ensures that there are lots of strategies for teams to learn and utilize.
4. Overall Matchmaking
As others have mentioned, please make it easier to find games when searching with a party. If I try to search in a party of more than 5-6 players it's literally impossible to find a game because the matchmaking parameters are still too tight. Why can I search TODAY with a full party in Halo 4 or Halo: Reach, but not Halo 5? Playing with friends is a fundamental part of the Halo BTB experience. After all, it's called BIG TEAM Battle. Please let us search with a BIG TEAM and find games with our friends.
That's all I have. Thank you again for listening to what the community has to say!