I'm a fan of Tudor (https://www.tudorwatch.com/) or Sinn (https://www.sinn.de/en/Kollektion.htm) for this price range.
I'm a big fan of microbrands--especially Chinese ones.
From perpetual watch co.: their "simple classic." Enamel dial and blue steeled hands: https://www.perpetual-watch.com/sc.html They service these too for a very reasonable price.
From Merkur: double tourbillions for $1000 (select black dial white index): https://www.merkurwatch.com/New-Pierre-Paulin-Luxury-True-Do...
From Tsar Bomba: Richard Mille style watches. https://tsarbomba.com/collections/mechanical
From Meisterstein (Germany), a tasteful watch assembled by a Glasshute trained watchmaker. https://www.meisterstein.com/uhren-1
From former Soviet style sold out of Germany: Sturmanskie OCEAN / OKEAN. https://www.poljot24.de/en/3133-1981599.html
Also from Japan: Japanese watches with special Japanese materials e.g. Arita Porcelain: https://www.seikowatches.com/us-en/products/presage/special/...
Also, a favorite dress watch: a watch that says I don't care too much about what the time is exactly: https://www.movado.com/us/en/shop-watches/museum-classic-aut...
Perhaps something from [Junghans](https://www.chrono24.com/junghans/meister-chronoscope--id290...)
Should fit your budget new. It might be more fun to look for used watches. If you're more interested in the inards, you can probably get a non working version to take apart for very cheap, but even a used Omega automatic should fit your budget.
If you want to "get into" watches it may make sense to read around a bit more to figure out what would suite your interests...
I went a different way. I researched what watch hobbyists wore while they mowed their lawns and dug ditches.
I landed on the clear leader, the Casio MDV-106[1].
Keep the rubber band it ships with, if you like, but most people seem to switch it out with a NATO or steel band.
It is such a great, sturdy watch and takes a beating and costs $30-50.
1. https://www.amazon.com/Casio-Stainless-Steel-Quartz-Plastic/...
Classy starter - Bulova Sutton - Skeleton https://www.bulova.com/us/en/product/97A162.html?cgid=mens
In this price range my recommendation would be Grand Seiko. There are microscope photos of GS and Rolex online if you search for it. You will never look at Rolex the same way ;)
It's great you're interested, but this is a bit of a broad question - imagine somebody said "I'm interested in cars, my budget is $50,000, what should I buy?"
Obviously you'd get people saying "Tesla", "Ford", "Peugot", basically replying with their favourite cars - and no regard to your own needs, or preferences.
Basically a watch is something you wear, something that is part-useful (it shows the damn time!) and part fashion. Beyond the standard "showing the time" there are complications. A complication is something additional a watch might do, such as show how much "wind" is left, show the date, show a phase of the moon, or have an alarm clock.
So as a bare minimum you need to think about the kind of complication you want, then about the type of watch you want. Do you want the date-display? If you want the date display that pushes you in one direction, if you don't that pushes you in another.
Equally there are three main kinds of watches quartz (i.e. battery-powered) which you've ruled out, automatics (which wind themselves), and manual, which you have to wind up yourself every day.
So .. a) do you want a date, b) do you want to wind, or have it run by magic?
After that it's a style question. There are broad groups of watches that share charactistics. For example a dive-watch is a watch that is underwater, and has a rotating bezel to keep track of time. A pilot watch has numbers in 24 hours, in two concentric rings. A drive watch is angled sideways. A dress watch is "simple" and "thin".
So again you need to think about what look you prefer.
With regular servicing a watch will essentially last forever. I have 40ish watches, some from recent years, some that are older than me. If you went to the ebay-of-watches, chrono24, you can find a lot of things. Just type "Vintage Soviet" and you'll find brands such as vostok which will sell you a used waterproof automatic for $100 or so. Equally you'll find brands you've never heard of, and watches that are 40 years old.
I'd suggest you start by buying one or two cheap watches. An "everyday" and a "special", to get a sense of what you yourself prefer. If you blow 2k on a watch it might be awesome, but you might find "Hang on, I hate roman numerals, they're not symetrical". Or you might have other issues.
Buying used, swiss, watches is easy but as a beginner you don't know what to look out for with regards to fakes and other frankenwatches. So that's another reason to avoid blowing a pile of cash on a single watch.
/r/watches is generally good. /r/rolex/, /r/vostok, and other brand-specific niches will often get circle-jerky, but can be useful resources.
Me? I pick watches that make me smile. I avoid roman numerals, I ignore anything with subdials (daytona-like) as too busy. But I genuinely love them, and have one for every occasion. Today I'm wearing an old Soviet watch from the 1950s, I bought it for €50 from Poland. Yesterday I wore a €10,000 Rolex Yacht Master. Tomorrow I might wear a casio terrorist watch. It's all about the enjoyment, the feelings, the style, and yourself. Less about specifics.
Happy collecting!
You can get a cool vintage Vostok for <$100
Grand Seiko
Try one of the mode dedicated forums like www.watchuseek.com.
Some pointers-
Mechanical watches requires periodic maintenance, it can get to 500$ every 5 years.
A movement is the watch's heart, many times different watches share the same movement. Some of the characteristics of a movement are manual vs automatic winding, power reserve for automatics (how many hours or days can it tick without winding it), functionality like day, date or second time zone. Accuracy can be slightly adjusted by a watchmaker and other methods but it tends to be much worse than digital watches- COSC certified watches, and those are not cheap, are allowed −4/+6 seconds per day.
Water resistance and design are important, for example some diver watches have screw down crowns.
Display backs are a thing, a transparent back showing the mechanism inside.
The type of glass or crystal will influence the price and scratch resistance, from just glass, through hardened glass (Seiko have some for example) to Sapphire with anti reflex coatings.
I am afraid that the really "cool" watches are out of your budget, but OTOH this is a nice budget for good watch.