Tikka is a good choice.
Howa is heavy and people have trouble with the stock being flexible. Has a reputation of shooting well (as does the Tikka).
The .22LR is for technique practice. Trajectory doesn't matter. JW15 is fine. For serious rabbit hare possum hunting the 17HMR or .223 are better depending on the type of country. Forte of the .22LR is it can be silenced, can be used on indoor ranges and ammo is quite cheap so you can fire 1000 rounds a year to practice. As a rough guide you should be able to consistently shoot 1" off a rest, 2" prone and sitting and 4" standing with your .22 at 25 m before you take your 308 out for animals.
Don't go for .223 or Grendel at this stage even for goats or fallow. They are lower power rounds for experienced shooters. .308 is a good all round choice. A beginner needs plenty of power. .3006 and 270 are even better to start with in my opinion. The same tikka action can take those longer cartridges OK.
I agree with the idea of using the doubtful alloy rings, no picatinny rail and no suppressor to start with. Upgrade later. Always use protection on the range and for goat bomb ups.
To be specific about the scope, I'd recommend a Leupold VX1 at the minimum but VX3 is preferable. Limit power to 7x or 9x top end. Burris, weaver, redfield and vortex do make good scopes but you need to start above the entry level grades, not go for the cheapest model. Sharp glass and bright transmission are not the most important features: you need strength, waterproofness, accurate adjustments, good simple reticle and a top notch warranty. This is assuming you don't have more than $1000 to spend. If you do, then post another thread asking about "first scope for centerfire" and you will get even more advice !
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