First, please accept my congratulations on contemplating the purchase of your first machine. Welcome to a great hobby!
Free advice is worth every penny you pay for it, but here goes: reluctantly, I'd agree that the Brunswick is probably the way to go--IF you have any interest in Edison diamond discs or Pathé vertical cut records.
Neither one is "core" collection material for the beginning collector; what you'll find in the average eBay listing or flea market or garage/attic/estate sale overwhelmingly is standard lateral cut disks on Victor, Columbia, (yes) Brunswick, and countless smaller labels. They're plentiful, and the common issues are cheap.
By contrast, you'll probably find Edison and Pathé records mostly or entirely by specifically searching for them on eBay or in mail/online auction lists, and for the most part any that would actually be interesting will be at a price premium over their lateral cut counterparts.
What you will almost certainly want at first, then, is something that will play conventional lateral 78s. The Brunswick will fill that bill, and it will also play vertical cuts if you wish to dabble in them. Brunswicks are nice machines, well built mechanically and as furniture, and there's something to be said for having one machine that plays everything. That said, the one time I've auditioned a Brunswick machine with the Ultona arm/reproducer, courtesy of a collector friend who owns one that has been properly overhauled, I'd say the sound was just so-so, not terrible but not as good as from a machine designed exclusively for lateral or vertical cut disks.
The Victrola, on the other hand, will play only lateral cut records, but all things being equal it will probably make them sound better than the Brunswick. The trouble is, the Victrola X is just about the most common model of the Victor uprights, and you'll almost certainly have trouble getting your money back out of it later should you choose to sell it. My thinking, then, is that you'd do best to get the Brunswick to start; it will do everything decently, albeit probably not best for anything. Look for a really to-notch, higher model Victrola to supplement it down the line, something like a Victrola XIV or XVI, for instance. Then the Brunswick can serve as your "vertical cut" machine, the Victrola your workhorse for laterals. If, after a while, you find yourself buying a lot of vertical cut records, at that point you can start looking for something more specialized like a good Edison diamond disc player and retire the Brunswick without having spent a fortune. If you decide that you simply aren't interested in vertical cut disks, again, you can shed the Brunswick (or just keep it for sentimental reasons). Meanwhile, you'll have something that will give you a lot of fun and enjoyable, if upgradeable, listening.
To close, if you're not clear about vertical vs. lateral or the differing styli for each, here are a few articles I wrote on the subject:
https://www.tnt-audio.com/vintage/mono-a-mono_e.html
https://www.tnt-audio.com/vintage/stylii_e.html
https://www.tnt-audio.com/vintage/stylii2_e.html