I'd recommend the 140 grain Nosler Partition Bullet. Regardless of the range to the game or the bullet velocity (within reason), this bullet will both open up/expand and penetrate deeply... and should leave you with a good blood trail that you can easily follow if the deer isn't knocked off his feet and killed instantly.
Good bullet construction is very important to you since you have the possibility of shooting at game at a great variation in range and, therefore, a great variation in bullet velocity. With your Remington 7mm magnum, your bullet velocity at 60 yards would be very high while at 300 yards, your bullet velocity would be considerably lower. Naturally, bullet velocity has a dramatic effect on bullet performance.
A bullet constructed to expand well at 300 yards (lower velocity) is not going to hold together at 60 yards (very high velocity) unless it is constructed in such a way that it will accommodate both extremes.
The Nosler Partition Bullet is such a bullet, I.E., it is designed with a "belt" inside the middle of the bullet effectively making the rear half of the bullet a solid that will drive deep into the vital areas without expanding while allowing the front half of the bullet to be constructed with a thinner jacket so that it will still expand well at lower velocities/longer ranges. This is why the Nosler Partition Bullets are still one the most popular premium bullets made.
Heavier bullets, like the 175 grain Remington bullet you are shooting now are generally constructed using thicker bullet jackets than the lighter bullets in the same caliber... and are designed for larger, heavier game like elk, bear or moose.
Heavy bullet with heavy jackets often will not open up and expand very well on smaller, lighter-boned animals like deer or antelope. When this happens, the bullet's wound channel is often only slightly larger than caliber-size and the bullet exits the animal on the off-side leaving only a caliber-sized hole which doesn't make for good blood trails.
If youd prefer a heavier bullet, Nosler Partition Bullets in 7mm (.284) also are available in 150 grain, 160 grain and 175 grain weights.
There are other well-designed premium bullets available, but I sincerely believe the Nosler Partition Bullet is still the preferred choice.
Good Hunting!
Ron T.