Do you currently own a rifle or are you familiar with any. Consider what makes you like or dislike any rifles you have used. For me, It's all about the features and feel of the rifle. I own several "hunting" rifles and my experiences with my current and past rifles shapes my wants for the new ones.
Things to consider:
Magazine type? I won't buy a hunting rifle that doesn't have a removable magazine whereas a hinged floor plate is perfectly fine for most people.
Sights? I always use a scope, but some people like to have open sights even if they have a scope, just in case.
Safety type? I prefer a 2 position safety that locks the bolt and has a button to release the bolt. I also like the safety to be mounted on the top/side of the action behind the closed bolt knob.
Action material? I thought I would prefer stainless for the barrel and receiver, but I now feel the best combination is a stainless barrel on a chromoly receiver.
Stock material? wood, plastic, fiberglass and carbon fiber are all common. I prefer synthetics on my big game rifles, but my shotguns and plinking 22 are a mixed bag.
There's a lot missing from the list, including the complicated matter of action mechanism and, if you choose a bolt action, controlled or push feed. I purposely didn't mention my reasons for my choices, because they are mostly just personal preference and shouldn't matter to you. All that matters is that there are a lot of different ways to make a great rifle, Tt's worth considering what options you do and don't want or care about before you start talking brands. I was interested in a Weatherby Vanguard, until I held one and fiddled with it. Nice rifles, just not for me.