As some others say, I would highly recommend a high quality 22 rimfire for "my 1st revolver"
Skills leaned with such carry over real well to all others, and more affordable practice quickly turns into more practice, an unbeatable combination.
Go with a DA/SA so you can experience the full range of revolver shooting fun.
Highest on my list of suggestions, would be any of the S&W k-frames (k-22/17/18), 4" to 6" barrel lengths, better triggers than most, outstanding reputation for accuracy. Nothing beats a good trigger for revolver shooting, all the rest is window dressing. Trigger control is where it's at. They can be found in your price range, if patient and look around.
Very ergonomic for nearly all folks, many grip styles readily available.
Excellent picture example in above post.
But if ye must go centerfire, then do also consider the centerfire S&W K family... any/all models in 38/357
Similar reasons, affordable shooting and very versatile in 38/357, so many ammo choices available for them, so easy found off-the-shelf ammo.
Centerfire k frames are abundant in the used gun market, anywhere from $250 to $500, real easy found.
Get one with adjustable sights; give yourself as many options as possible with your 1st revolver.
In either case (any case), go with a full size all steel revolver, no snubbies or liteweights no matter how cute they be.
Leave the shorties for "my 2nd" or "my 3rd"
Good luck, and welcome to he wide world of wheelies !
PS
and don't be walking too quickly on by any finds of nice old Dan Wesson or Ruger "six" series centerfire DA revolvers
Colts, good 'uns are great ones, but scarcer and pricier
(and leave home-boy gunsmithing to bubba, unless you be a real gunsmith... or you be bubba)