1. Define the types of quarry you intend to hunt (if you're choosing a bullet for hunting). Quarry type influences terminal-ballistics requirements. You wouldn't want to shoot a grizzly bear with a varminting bullet.
2. Decide what ranges you want to shoot at. Some bullets (e.g. flat-base target bullets) are extremely accurate at 100 yards, but perform poorly at 1,000 yards. Others really shine at long distances, but (supposedly) don't stabilize quickly. Long distances favor heavy-for-caliber bullets requiring a barrel with a fast twist rate. What "fast" means depends somewhat on the caliber, but usually means something around 1:8. For example, the 6.8 Western is designed around long-for-caliber 270 bullets, so it has a 1:8 SAAMI-spec twist rate. The more traditional 270 Winchester has a 1:10 SAAMI-spec twist for bullets of the same diameter.
3. Decide whether you want or need to hunt with a lead-free bullet. California and other places don't allow lead bullets. If so, you'll likely use "mono" bullets, i.e. solid-copper bullets. There are debates about how well these perform compared to cup-and-core etc. bullets with lead inside. (You can read these debates on this forum.)
4. Pick a hunting-bullet philosophy. Some folks believe in bullets having high penetration (Nosler Partitions and Accubonds represent two types of bullet construction that favor deep penetration), others believe in bullets that penetrate a few inches and then fragment violently (such as Berger bullets). (Another debate.)
5. Pick a single bullet that exemplifies everything you want along the above dimensions. Buy or build a rifle that is best suited to that bullet.
6. If you're handloading, try different components (powder, primer, case) and specifications (COAL, powder charge weight) to shoot that one bullet as accurately as you can.
You can vary the above procedure a bit to be a "one rifle hunter." (There's a thread on this forum on the subject, of course.) Faster twist rates can still shoot lighter-for-caliber bullets accurately (contrary to popular belief), and if you only hunt at high altitude, you can get away with a lower twist rate and still stabilize long-for-caliber bullets. For example, a 300 Win Mag with a 1:10 twist rate will shoot 165-grain bullets (really fast!) at antelope, 180-grain bullets at deer, and 220-grain bullets at elk. Then you have to choose three bullets for one rifle.
I build each of my rifles around one or two bullets. For big game I mostly design around heavy-for-caliber Berger hybrid hunters or VLDs: 156-grain EOL for a (1:7.5 twist) 264 Win Mag, 168-grain VLD for a 280 Rem (which I think of as a short/medium-range "woods gun"), 180-grain VLD for a 280 AI, and 210-grain VLD for a 300 RUM (which I'm changing over to a 1:9 twist barrel, so it shoots 230-grain bullets). I load for these rifles so they all have essentially the same drop chart out to 600 yards, which means I only have to remember one drop chart.
The above approach has given me eight rifle-bullet combinations I'm very happy with. All of my center-fire rifles shoot 1/3 MOA or better. The quarry mostly drop right where they're shot. Having the right bullet for the quarry and distance is a real confidence builder.