I know how you feel. I grew up in Ohio, and it too is shotgun only. I didn't start shooting rifles until I was in my early 30s. I still don't know much, but I'll share what I have learned.
The Barnes TSX bullets are great based on my experiences. These bullets are what some call "monolithic" (wrong use of the word, but it seems to be widely accepted). They're constructed entirely out of one alloy no core material such as lead surrounded by a different jacket material, such as copper.
These bullets have a small hollow point which helps initiate their classic 4-pedal expansion. Weight retention remains near 100% and penetration is incredible. I've only recovered a few, and all have been frontal shots and the bullets have been recovered in the pelvic-bone region (whitetail, axis, zebra). All were near 100% weight retention and all had expanded as designed.
The argument will go on for years to come over what's better - tough bullets that retain all their weight and blow thru the animal vs. bullets that penetrate, then expand significantly, even come apart, and "dump all their energy" into the animal. Regardless of what camp you're in, at least one criteria must be met - the bullet better be constructed well enough to break through bone on the side it is placed and still penetrate deeply enough into the chest cavity to kill the animal efficiently. Personally, I like a bullet that will break bone on the side it is placed, pass thru the chest cavity, and then break bone on its way out the other side. Animals hit this way seldom go more than a few feet - like what can be counted on one hand. If bone is not hit, there will be blood coming out both sides. If the animal is facing you, chances are the bullet will penetrate almost the entire length of the animal.
The Barnes TSX certainly isn't the only premium bullet out there that will penetrate deeply and stay together. Remington factory loads 180 grain Swift A-Frames, and the A-Frames have a great reputation in both Africa and Alaska. The Nosler Partition also has a good and long reputation, but I quit trying to use these years ago because I could never get a decent group with partitions out of any of the rifles where I have tried them. Before switching to TSX, I used Trophy Bonded Bear Claws. I've taken deer, elk and moose with the Bear Claws. They didn't offer the same penetration as the TSX, but they stayed together, expanded well and penetrated well (recovered many just under the skin on the opposite side).
So far I have yet to own a rifle that will not deliver MOA accuracy with TSX bullets, and this certainly factors into my passion for these bullets. I tried the tipped TSX from Barnes in my .300 Win, but I can't get better than a 2" group with the TTSX. The TSX in this gun will print sub MOA. A few years ago I thought the Barnes MRX was the key (has a tungsten-alloy core that is near the base of the bullet and a great ballistic coefficient). I shot a caribou on the tundra that was quartering towards me at 285 yards. The bullet broke the on shoulder, but there were 2 exit holes about 8 inches apart on the off side. In some form or fashion, this bullet with two different components came apart after hitting the onside shoulder. I've chosen to stick with the TSX, and my kids and I use these in everything from a 6.8 SPC to our .375 H&H. I use these in a 9.3 X 74R double as well.
If you tell your PH you're using Barnes TSX, Swift A-Frame or Nosler Partition, he'll be quite happy. As many have suggested, Barnes now markets a Tipped TSX (TTSX) and there is a Tipped Trophy Bonded Bear Claw. Because many "tipped bullets" are designed for target or varmint shooting and not constructed for big-game use, guides and PHs may appear apprehensive if you pull out a bullet that has a "plastic" tip. The TTSX and the tipped TBBC are still fine, premium bullets, but the originals without the pretty-colored tips will be accepted immediately with no explanations needed from you.
In .30-06, prices for even the premium bullets are not too outrageous. I would experiment with the premium bullets and determine which one your rifle likes best. Once you've determined that, by all means, shot often with cheaper bullets to get comfortable with the use of a rifle. After using only a shotgun or muzzle loader, it takes some time to get accustomed to a rifle. The recoil is mild with a .30-06, but it is sharper than what a shotgun delivers. Just understand that sometimes the cheaper bullets may not deliver the accuracy that you got from your chosen premium bullet. Sometimes that can be discouraging as you practice from various positions (is it me or is the bullet?).
There are tons of articles on various websites on how best to practice. The reoccurring theme is "get off the bench". Get some shooting sticks and use them. Load the magazine fully and cycle the bolt often to both get the feel of it and to ensure there are no feeding issues with your rifle. Get accustomed to cycling the bolt and getting back on target quickly, regardless of how the first shot went. I can say all this because it is all stuff I still struggle with!
Good luck. Planning the first safari is exciting!
