Also, would it be better for me cost-wise to go on month-to-month with TMo and pay $20-per-month for the S4? Rather than paying the higher monthly bill from Verizon or someone else? Even though I am paying more for the phone, ultimately I am saving money on the monthly bill I would assume.
You'll want to sit down and do the math, particularly comparing the plans, based on your data usage. All things being equal, you're probably better off with T-Mobile price-wise, but the issue is really if all things are equal.
Let's begin: T-Mobile got into trouble (read: lawsuits) for the way they were advertising the whole "no plan" deal, and they've actually changed their advertising. Look at their website now. They explain that you're basically just buying the phone on time, as you would if you were buying a car or getting a mortgage. You've got a $99 downpayment on the phone plus two years of payments at $20 each. Total is $99 + ($20 x 12) = $339. Now, you can buy the phone from VZW for $249, less a $50 rebate, so that's $199.
VZW looks like a better deal (by about $140). But is it that simple? No. VZW may be rolling that extra $140 into the monthly payment.
T Mobile will charge you $50/month for unlimited talk and text, and 500 MB of data. If you want 2 GB of data, that's $60/month; unlimited data is $70. (Whether and when they throttle your data speeds is outside the scope of this post.)
Now, VZW's "Share Everything" plan is going to be $90/month for 1 GB of data (plus unlimited talk and text), $100/mo for two GB, and upwards from there (they don't have an unlimited data plan unless you're grandfathered in).
Suppose you want 2 GB of data for month (as that's the easiest comparison). T-mobile is $60/month; Verizon is $100/month. That's $40 more per month. Remember where VZW was charging you $140 less for the phone? That's eaten up in the first four months
of charges on the 2 GB plan. Two full years on the plan and you'll end up paying VZW a whopping $960 more in plan fees ($40 per month times 24 months). Sorta makes that $140 difference in the price of the phone look insignificant.
Now, you may do this math and think, "Holy cow! I should totally go with T-Mobile because that will cost me $820 less over the life of the phone!" And that may be true. OTOH, that option doesn't exist for me, because there's crappy T-Mobile coverage in my neighborhood. Seriously crappy. I'm not talking slow data speeds here; I'm talking about nobody with T-Mobile can get a phone signal in my house -- and even when they go out to the driveway, they get maybe 1 bar and the call frequently drops. So I say to myself, "Self, do I want to save $820 or do I want a phone I can actually use?" For me, it was very clear that I had to go with VZW (and, believe me, I say this as someone with a deep abiding hatred of VZW), because they're the only ones with viable coverage. They say "It's the network," and, from where I'm sitting, it really is. So, I mean, I don't look at it as VZW charging me extra for the phone; I look at it as VZW charging me extra to use a network that actually works where I live. I hate it, but that's how it is.
Anyway -- those are the sorts of factors you're going to want to look at before you make the call.