I would encourage you to mine Facebook Marketplace. You can find really nice cues for $100 or way less.
If buying new, get a butt with few cosmetic embellishments like inlays. They add to the cost without adding any performance. I’d recommend a 18.5-19.5 oz cue, somewhere around 12.5mm tip. This is middle-of-the-road and should serve you well until you develop and know your preferences for an upgrade later.
As a beginner, getting a custom-ordered cue seems overkill to me; you don’t yet know what you like. Forward-weighted or Butt-weighted? Linen wrap or leather or no wrap? Taper? Tip diameter?
Ideally you can find some used cues and if you are lucky might even be able to hit a few balls on the owner’s table if they have one to see if you like how it feels.
Try to find one with a very common joint so you can easily upgrade later to a different shaft.
Best of luck.
FYI, my frame of reference: I've been serious about playing pool for about three years, joined leagues. I'm an APA SL6.
My playing cue is a vintage Adam, with zero cosmetic embellishments. Just a plain wooden cue with a linen wrap, fairly common 5/16"-18 joint. Someone gave it to me. It has a plastic joint, so it's slightly more back-weighted (by about 1.5") than my other vintage Adam. I also have a vintage Adam, circa mid-90s, I think. It has a metal joint, so it's weighted slightly more forward. The first one was free; the second I picked up via FB Marketplace for $80.
I can play these two cues interchangeably with a common shaft (getting used to the balance point is pretty quick) although I have stuck with the older Adam the last three months and don't plan to switch back and forth. Last November I bought myself a birthday/Christmas present, and had Ed Petersen (EAP Cues) make me a CF shaft for $265. I LOVE IT!! It has a Kamikaze Elite soft tip. I really do love it.
I have also owned a Meucci 97-1, which I eventually sold. Nice cue, but I never gelled with it. It had the slightest wobble in the shaft but that's not why I didn't like it that much.
I had a Heubler I also found on FB. It had a weird taper I did not like, and had an annoying (to me) PING. I sold it. I did not lose any $$ on either the Meucci or the Heubler, and I only sold them for what I had in them (I probably could have gotten more.)
My break cue was also given to me by the guy who gave me my Adam player. It's probably a Chinese knock-off, has decals to look like inlays. It hits about the same as my Adams. It's nothing special but it's OK. I have a hard tip on it.
Moral of the story: I'm sure you can find something local for cheap, then possibly upgrade it later with an LD or other shaft.