Actually, yes we jumped to discussion of 375.
Lets assume two things.
Lets assume that OP is experienced local hunter, that already has good rifle inventory, with main to go 30 cal. (Americans call this "deer rifle")
Lets assume next that he will not immediately go for buffalo hunt, but he will settle to plains game safari, as his first safari
So, in that case, he can as well take his good old trusty all round rifle, 30 cal. Make good choice of ammo, and go to first safari.
Or optionally to rent.
That being said, my experience was:
My first safari on PG was with camp rifle, and in 375 HH. (I fell in love with the caliber)
By the time, I completed my 2nd safari (with rental mauser in 300 HH), I had it all figured out.
I had buffalo, eland and whatnot on my mind, and was fairly certain I will keep going on safaris till as long as I can afford, and then I went for 375 HH as my dedicated buffalo gun and African allrounder.
Now, rental rifle or not that is the question?
It just happened to be that in my first two safaris when I hunted with rental rifle, I was not familair with rented rifle.
First one had too light trigger, and second one had too rough double stage trigger.
So, in both cases, although I tested rifles on the range before hunt, my first african animal was wounded.
First hunt, I wounded oryx, later found. This was first shot and first animal in Africa for me.
Second hunt, first animal on safari, first day, I pulled to hard, and hit low, (180 meters) and wounded in leg. Tracker found and we collected later. impala
So, I never lost an animal, but first shots with unfamiliar rifles were not perfect.
2nd day, on any safari was always better.
Last day of safari me and rifle, rented or owned are one being.
So bringing his own 30 cal rifle on safari, will make him fully effective on day one. No surprises.
Rented rifle brings also a possible flaw of being issued with cheap low quality ammo.
So, if OP has his good old gun for boar and deer, he can take it on first safari.
later to plan for something specialized. 375 hh recommended, provided that he "promises" to hunt bufallo, one day in the future.