Once upon a time, Browning was top-shelf stuff. I have a '60s-vintage A5 shotgun whose fit & finish are amazing. But times change - the A5 is a kick-like-mule dinosaur and newer Browning shotguns... meh. You did well to check in here.
I'm not quite four years into this precision rifle stuff after a few decades of shotgun competition and a lifetime of shooting. I started off with a pair of Tikkas and moved to Remington 700 footprint customs. I'm retired and have spent a lot of time and $ learning the stuff that you're looking at now.
You said this will be a range toy. What range? For 500 yards or under, a .223 is superbly accurate and cheaper to shoot than larger calibers, and has great barrel life. For 200 yards or under... [shrug] I'd get a nice .22 and feed it good ammo and screw the centerfires unless you just want one. That's just me, because I'm so addicted to this silliness that shooting centerfire at under 500 yards just seems pointless unless you're into F-class and such. Also, if you don't intend to shoot more than a few boxes of ammo a year, maybe a sub-$750 rifle will work just fine for you.
With that said...
If you want a top-shelf factory-built range toy that has ample aftermarket support at a sub-$2000 price point for the ready-to-go rifle sans optic - it's extremely hard to beat a Tikka.
If you go $2000 and up, you can look into the "factory customs" from MPA, Defiance/Badrock, etc. which all have Remington 700 footprint actions, which means you get easily swappable bits to upgrade, resell, etc. Example: Let's say you buy a Badrock Southfork rifle, which I believe is based on the Defiance Tenacity action, for $1995 fitted with the MDT LSS-XL Gen-2 chassis. You decide to get into PRS... the LSS-XL chassis is nice (I had one), but it's an older, entry-level design. So you can upgrade to any other R700 chassis (or stock) and swap it in in 20 minutes tops by removing/replacing two screws. Same with triggers.
Tikka absolutely has lots of aftermarket support - just keep in mind the bits are Tikka-specific. Building on the above example: Buy a Tikka T3X in whatever flavor, ditch the horrid rubber stock, and replace with MDT, MPA, KRG, whatever. Plenty of stock/chassis options. Not quite as many options for trigger upgrade, but Tikka triggers are quite good out of the box. You'll also need a good picatinny rail for scope mounting on many Tikka models. But the barreled actions are great.
Sure, you can absolutely buy rifles for $500-600 or even less and put time, money, and effort into making it what a Tikka would be when you take it out of the box. And it will still resell like a $500-600 rifle regardless of $$ you put into it, and unless you pay $$ to a good smith, compared to a Tikka it's going to cycle like dragging a crowbar through a keg of nails.
If all you're going to do is shoot half a dozen boxes of ammo a year at 100-200 yard range, spending more than $1000 for a centerfire rifle would be like buying an Audi A4 to drive to the grocery store once a month. Nothing wrong with it, but a stripped Ford Escape would be more than enough to get the job done.
Welcome to SH. There's a gold mine of info here, and for someone new to precision rifle, it can be overwhelming. Take your time to learn, accept that you'll buy and sell a bunch of stuff, and enjoy the ride.
www.browning.com 
