If lever guns are your thing then go for it. Marlin still makes a nice lever gun despite their recent troubles. But I might look elsewhere because of the problems with customer service. You can go with a Henry which has great CS but IMO they just aren't the most accurate guns on the rack.
Personally I like bolt action guns because that's where the accuracy is. If I liked plinking with a lever gun I'd buy a Henry Golden Boy and then buy a really good rifle to hunt with.
You never mentioned a budget or anything about glass or what all you would be doing besides shooting small black tail deer. More information would help. Personally I live Savage and CZ for great values depending on what you want and what you are looking to do in the future. For a light weight hunting rifle I'd probably go with a CZ 557 or maybe a Tikka T3. For more serious target work I'd get into the Savage chain and work my way up the ladder if that's what it took. Personally I just jumped in a bought one of their best rifles right off the bat to avoid the hassles of building a platform. All that testing of ammo every time you make a change can really add up. It's fun but expensive.
So again your budget and your intentions would be important.
You can buy a rifle in the Savage line for
$440 then work your way up with modifications. You don't even need a scope for that particular rifle since it actually has iron sights (rare these days). It's a great place to start and upgrading a Savage is a lot like upgradging a 10/22. There are lots of ways to go and you can end up at a really good place.
You can get a CZ 527 for
under $550 but it will require a scope. Figure at least $250 for a decent scope close to the quality of this rifle. Maybe $200 if you won't be doing real long range work.
Notice I picked a .308 and a 30.06 for my choices here. For hunting I think you can't go wrong. If you want less recoil go with a lighter recoiling cartridge. You'll have the ability to shoot bigger game if you ever want to do that. With the Savage you can of course start with a different caliber and change it as your mood and your bank account changes.
Then there's the Tikka. The T-3 Light can be bought for
under $540 in .308. Lots of people really like this rifle. All of these are excellent rifles IMO. And so are rifles made by Howa, T/C, Ruger, etc. etc. etc. etc.. There are way more choices than I have time to describe. The ones I mentioned are the rifles I seriously considered buying or have bought at one time. I don't actually have one of these models I guess but I have 2 Savage rifles in the 110 family. I came very close to buying the Hog Hunter I mentioned here at one point. I've wanted a Tikka for quite a while and I have another CZ rifle I really like not to mention all the other CZ products I've seen that were all excellent. My friend thanks me every time he sees me for pointing him to a CZ handgun. He's won several competitions using it.
The world is full of good rifles. Go to the shops and find examples that fit you well. Check for the features you like. If you don't know what you like do some research. What kind of safety setup do you like? Is that important to you? 2 position or 3 on the safety? Personally I think 3 position is hard to beat. It gives you serious advantages.
There's a lot of research to be done if you're just going to buy one rifle that will be your only rifle for a while. My way of dealing with things has always been if I can't decide what I like buy all of them I might like and sort them out. It usually ends up I like all of them though. Funny how I never seem to sell any guns but once in a while I do. Usually it's when I have more than one or two of the same type of gun. Some of my cheapest guns will be the ones I hold onto forever or until I pass them on to one of my kids. I've already started handing them down just like my dad did for me.
Asking gun junkies to pick just one gun is like asking a heroin addict to limit himself to one fix the rest of his life. I think I'll go do some shooting now.