Is the caliber capable of ethically killing a deer? Yes, with the right type of bullet. Many deer have died under this caliber over the years.
Are you capable of killing a deer with this caliber? T
hat depends on your dedication to practice and accuracy, ability to choose the right type of bullet setup for your game, and knowing your gun's and bullet's limits with that game and sticking within those limits. (Like required of any gun of any caliber.)
Will a larger bore be better? Yes and no. If a larger caliber with greater recoil and possibly heavier overall weight will cause you to flinch from the recoil or be uncomfortable shooting then no, that caliber wouldn't be better, because you'd be more prone to shooting inaccurately. No matter what caliber you stick on a gun, if the shooter cannot be accurate with it, the deer isn't going to die any quicker than a smaller caliber shot accurately would kill it. Like they say "A dead deer is a dead deer...there is no better case of death possible once it's dead."
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With all that said, I've been hunting whitetails with a .243 Win since day one and still do. I have confidence in my gun and wouldn't trade it for the world. Now on the same hand you don't see me going out bear hunting or elk hunting with this caliber. This is only for deer and predators and I will never use it for anything besides that. I know my limits and I don't cross them. The day I do cross them is the day I become an unethical hunter.
I've never lost a deer yet and most, if not all, of my kills died within 50 yards of where they were shot with a single well placed bullet. I've only had one deer that I didn't heart or lung shot on with the first bullet and that wasn't gun nor caliber error, but user error when younger and with a good followup shot I still had that deer down within 50yards. Several of my deer have even dropped in their tracks and had massive internal damage from the shots. To the point where the butcher did a double take when he saw the damage and found out what caliber gun I shot it with.
As far as bloodtrails go, I've experienced great blood trails on a few and good bloodtrails for the most part from all my other deer. I've only had one fluke instance of minimal bleeding from a perfect heart shot, due to organ blockage of the entrance and exit wounds. With that said, any caliber can experience a fluke instance where an organ or piece of blown up organ will plug the entrance and/or exit wounds up and prevent a good bloodtrail and minimal bleeding, yet be a well placed vital shot that brings the animal down. That's all part of hunting and needing to not only be a good hunter, but tracker too. No matter how good a shot you are there is always a chance of minimal bloodtrails and still having a vital shot on the animal. You should always try your best to track every animal you put the crosshairs on and pull that trigger even if you think you clean missed. Bloodtrail isn't a very good indicator on a dead animal. I've seen many times bad shots that were not lethal on animals bleed quite a bit and fool a hunter into thinking he has a dead animal to find out otherwise or lethal shots that bled minimal and the person thinks he didn't kill the animal, but finds it dead not very far away.
As far as equipment for a .243 Win there are a lot of good choices out there. I'd recommend going to a gunshop holding several different brands and models of guns in your caliber and finding one that is comfortable to hold in your price range. As far as bullets do your research find out the distances you'd like to try shooting out to and pick a bullet that can give good killing power out to that distance. Then try it in your gun and see how your gun likes the round. Not all guns like the same rounds of bullets and perform as well with them as the next, even guns of the same make and model. So, you may try a couple different brands and styles until you find one that will be accurate enough for you through your particular gun.
My gun is a Remington Model Seven SS. My gun is fitted perfectly to my size and I'm extremely comfortable shooting it. I shoot 100-Grain Federal Classic HI-SHOK soft points in .243 Win. Practice and good shooting is a must with any caliber rifle. Know your limits on not only your bullet's killing power out to certain ranges, but your own accuracy with the gun out to certain ranges, and don't cross it. But, that should be common sense for any caliber gun used for hunting any animal.
Good luck and hope you find yourself a gun that makes you happy and gets the job done!
