With a 375 H&H you do want a bit of weight - but balance and fit more important than weight per se. Magazine - make sure its robust. You don’t want it going bombs away under recoil.
And it must feed reliably each and every time. There is always a debate over controlled round feed vs push feed. But provided the rifle and feed rails are set up properly and it feeds and ejects well its probably a moot point. Good technique on the part of the user to avoid short stroking is essential regardless of action type.
375 has enough recoil that good scope mounts are required. Aluminium may be ok for smaller rifles, but solid steel is the correct material for a 375.
Scope - very much depends on what you intend to do with a 375. They are perfectly capable of shooting plains game / deer out to 250m, but equally you do want plenty of field of view. The 1.5-6x42 is probably pretty close to perfect, but good case can be made for a straight tube 1-4 or 1-6x20. Key though is to have a proper cheek weld and sights align where you look. Depending on how good your eyes are and how well you can use them, you may or may not want to have or use open sights. Which may or may not dictate whether you want detachable scope mounts.
But make sure the scope / scope mounts all plenty of access into the action. I would not put a full length rail across the top for example. And make sure empties don’t hit the scope and bounce back into action.
Handling - a 375 should handle and point well. Think a fine shotgun. It should fit and sights should align where you look. A lot of use of the 375 will be bigger game at closer range. Opportunities will often be fast and you need to hit a dinner plate sized target.
A long cumbersome rifle with heavy moderator and no weight in the stock is fine on the range shooting prone. Not what you need for an off hand or off stick shot at the kudu of a lifetime before it melts back into the bush.
Trevor Procter, Rigby, CZ etc all pretty much got it right. CZ / Brno’s are good tough guns, but often need a bit of fettling to improve. Sako’s are a bit light. The CRF Win Mod 70 is a classic and are nice handling rifles. Rem 700’s are affordable and any long action 700 will take 375 H&H. But may need some work to make reliable. A 375 barrel on an R8 or R93 may be an option if you already have that system. Depending on barrel weight may be a bit light.
... but I bemoaned the minimal ammunition capacity, Now I'm on a straight pull Merkel Alpinist 9.3 x 62, employing two x 5 round box mags.
