What is the benefit of a wireless gateway vs. high speed modem?

do you mean wireless Router when you say gateway?

if so then the main difference is that the wirless router acts as server providing an internet connection to one or many PC's/ Macs via wired or wireless connection.

It contain a build in DSL modem and can be on all the time and if you computer has a wifi card then it can connect to the router from anywere with in range.

A straight modem will most likely be a black box that connects directly to you computer via usb or some other method and acts as a direct connection to the internet, it cant usually be shared with other computer or a network withought turning your pc or mac into a server and setting as the default gateway for the network. It also means that that computer has to be on all the time for anyother computers to access the internet.

I think it’s useful to know there are a few distinct functions involved in domestic internet connectivity. Armed with that info you can decide what kind of internet service suits you. A typical domestic internet installation has one or two boxes that include at least three or four functions.
a) the modem; communicates with the ISP’s network over DSL(phone lines), coax(old-style TV cable), optical fiber(e.g.FIOS), radio with a satellite (e.g.Dish), and radio over cellphone networks. Often this part a) is standalone, except when you go over the cell networks where they almost always combine all the functions mentioned below too.
The stuff you’re trying to decide as far as speed is based on the above part of the package.
It’s dependent on the medium (wire, fiber, outer space) for the speed and reliability and even cost.

Often all of the below functions are often in one other box: (sometimes all of the below are combined with the modem above in one box, e.g. when the connection is over cell networks).
b) the router; this function bridges your home network traffic to the outside. The outside-facing portion of this will appear as one machine/ one address to your ISP. The inside-facing portion acts at the ‘gateway’ to the internet.
c) Network Address Translation(NAT); this function allows several machines on your home network to funnel through the gateway as one stream.
d) hub/switch; there is often a four-port hub that lets you connect multiple devices to your internal network. For a lot of people this hub is the internal network.
e) WiFi; This function allows gadgets to connect to the internal network over short-range radio(“wireless”) instead of plugging into the hub. Any hub you get today should be using the “N” standard, or better, for speed.

The OP descriptions sound like :
cheap and slow option a) that plugs into the wall (15.99$).
Fast option that plugs into the wall (50$).
Moderate speed option that does not plug into the wall (80$), uses cell-phone network to connect to the internet. Portable but vulnerable to quality of cell-phone service especially for high-bandwidth like watching netflix. I would advise against this third option unless you really need to haul your internet connectivity around with you. Some smartphones can do this if the data plan allows ‘tethering’. Most of the cell-phone-based offerings have bandwidth caps per month or hefty charges for high usage.