The great thing about BST is it is highly customizable to suit YOUR tastes. I'm personally a solo only BST. Keep in mind that your gear isn't soley to benefit you, there should be some focus on your pet since he/she/it is a major aspect of your job. That being said here are some of the sets I personally use:
Reward:
The idea is to reach 50% cap (which can be done with Monster feet +2 zoraal ja's axe and Ogre Gloves) then use recast down gear (khimera bonnet/monster legs +2) and fill the rest with MND.
General TP:
The axes change depending on what I'm doing situationally. If you want pure DD go with STR Astolfo/DA +11 axe or pet tank use -11% Pet PDT (which you need x2 anyway) or mix and match pet MDB or EVA.
PET doing all the work
Anwig is pet 5% haste -10% PDT Mirke is Pet attk/DA and adaman sollerets have -6 Call Beast delay pet haste +3% subtle blow +5. Beast Bazubands would be nice in the hand slot if you can manage to find Dragonscale Bugul Ja.
Ruinator
Debating if STR from pyro beats chance for DA/TA proc from epona's.
I have LOTS of other situation sets but these are just basic.
Merits I have 5/5 Ruinator, Reward recast 5/5 Call Beast 5/5, Feral Howl 1/5 (just to have it to chance proc in dynamis) Beast Affinity 2/5 (with monster gloves this should be enough to cap all new jugs save for nazuna at 97-99) Beast Healer i have 4 in but swapping merits around lately to focus more on killer instinct which will probably end up 3/5 at least.