As a general rule of thumb, having a sectional density (SD) of .300 or higher is more desirable because it means better straight line penetration for the given bullet, even if it's an expanding one. To get a .375 caliber bullet above the .300 SD line, the bullet needs to weigh 300 grains or more. A 260 grain bullet has a .246 SD.
Most companies make 300 grain .375 caliber bullets and I'd highly recommend the Barnes TSX, Swift A-Frame, Federal TBBC and Norma Oryx. Norma has loaded ammo up to 350 grains and I believe Rhino makes up to 380 grains if you can get your hands on them.
As for solids, you should absolutely take some but only load them if your PH asks you to. Matter of fact, you should consult your PH on what his recommendations are for .375 caliber bullets for buffalo.