Greetings,
My vote is for the .22RF bolt action. At this stage you both need practice and lots of it. Your pick of the Tikka T1 is a good one especially if your second rifle is also a Tikka. Make sure it comes suppressed. Also ensure that the scope is either a rimfire model or is able to be focussed for distance. At 11 your assistant hunter is still growing so he needs to be able to shoot it as well even if it is just off a rest. If he is still a little chap then a cheaper S/H .22 for him with the stock cut down to suit him might be considered.
As far as a first centrefire rifle goes there are oodles of options. I am a little torn between a .223 (with an 8" twist barrel) and a .260/ 7mm-08 or a .308. Any of these, if suppressed and with a decent recoil pad, will do the job. If hunting for deer is on the menu then one of the bigger ones would be best but the .223 shines for lighter game and longer range than the .22RF.
There are no wrong choices.
Regards Grandpamac.
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