While I won't necessarily disagree with the "spend $175 on the vise and put the rest into mats" philosophy...I also would stop short of unequivocally saying to do it that way.
More accurately, I'd ask you how confident you are that tying will be a lifelong hobby/pursuit/passion? And how seriously you expect to get into it.
I ask because while that $175 price point will absolutely get you well beyond the "entry level", and into vises that will serve you well your entire life...if you can budget $350 for a vise, you're likely going to be able to pick up materials as you see fit without much in the way of financial hand-wringing, and mats are the kind of thing that if you only want to spend $10-20 at a clip, you can do it. You can't exactly buy vise like that.
Further, while $175 will get you a LOT of vise, and you wouldn't need to ever upgrade, at that price point, the time may come where you'd like to upgrade. For me, in that $250-375 range is where vises seem to go from "top of the line functionally" into "extravagance" (that's just me personally, though...some guys may consider things a functional upgrade that I'd consider "flair", while others may look at things I consider functional as frivolous).
Obviously, it's up to you, but the way I tend to look at things, if I were in your shoes, I'd probably be looking at $250-350 vises...that gets you into things like the Dyna-King Trekker, the Renzetti Presentation 2000 series, and just about any Regal short of the Revolution (and even there you could swing the clamp model). Though with that said, it's also true that this is with hindsight, knowing how much I like to tie. If you're not sure, or you only plan to strictly tie the bare minimum to put workhorse patterns in a box, then I couldn't justify the extra spending.
Just something else to think about!