My own advice mirrors NM Shooter. Minimum caliber - .25. I'm using a .22 which theoretically has nearly the same ballistics as a .25, but it just can't seem to hit 100 yards. Same experience as NM Shooter. Shoots extremely well at 50 to 75, but not 100 yards.
To give you an example, my Marauder shoots 1.5 inch groups at 75 yards, and part of the spread is the shooter, not the gun. At 100 yards, same exact setup, 6 inch group, and it looked like the pellets may have been tumbling before they hit the target. Still not sure what's happening, but will investigate further. Choose a gun that is known to hit 100 yards consistently, don't cheap out here.
Budget wise you should figure on (Don't let me scare you off, yes it's a big investment, but your ammunition costs drop tremendously, from whatever you are shooting now at probably $.50 to $1.00 per round to literally pennies):
The Gauntlet looks like a good gun, but, as with a Marauder, it's an entry level gun. You may want to figure more like
$800 to $1000 for the gun. Or, you could figure your first gun is a learning platform and plan on replacing / upgrading within a year or two. I own a Marauder with that same idea in mind. Saving for my "Upgrade" to a Crown now. Marauders can be tuned and worked on to get to the magic 100 yards, but others come out of the box ready to go. Marauders come in at around $500 or a bit more where an FX Streamline hits $1000.
$
350 for a 90 CI HPA bottle. This is the smallest you should even consider. Other tanks go up from there. This bottle provides around a dozen refills on my Marauder, with a 215cc cylinder. 500 CC bottle guns get half the number of refills. For me, that's between 200 and 400 shots depending on how I have the gun adjusted.
Scope - if you have a scope with parallax down to 15 yards or so, you are set to go. You'll need mounting rings as most rifles are Weaver / Picitinny where air rifles are 11mm Dovetail. Rings range from $6 to $150 depending on what you want. If you need a scope, my personal current favorite is the BSA 4-14x44 FFP that's selling for about $140. That would be the low end and represents one savings for air rifles. I'd never put that on a high powered rifle, as I wouldn't trust it to hold zero. On a PCP, no recoil to speak of, so much easier on scopes. Or you can buy the current, high end, favorite of some people, the Viper Pro series at around $800. I'm a cheapskate, so looking more at the BSA variety.
Now is the hard question.
Pump, Compressor, Paint ball / Scuba Shop? If you like to shoot, forget the hand pump. The 215 CC Tank on the Marauder takes about 3 to 5 strokes per shot depending on how the gun is adjusted. That last 20 to 30 strokes are a real bear because you are pushing 2700 to 3000 PSI resistance. If you have a paintball shop or scuba shop nearby, check them out. I have one and it's around $5 per fill on the 90CI tank. If you buy a 80 Cubic Foot tank, it's more expensive, and some shops just won't fill them, so check that out in advance.
Lacking a paintball shop, you may be looking at a compressor. I'm no expert. Having said that, we see a number of possibilities.
High End - Daystate Compressor. $3000
Mid range - Omega $1400 to $2300
Low end - I like this option - Cheap Chinese compressor off eBay or Amazon.
Ranges from $320 to $400 shipped and in your hands. Read the thread
http://www.airgunnation.com/topic/did-i-make-a-big-mistake-i-bought-a-yong-heng-compressor-from-china/ - It gets good reviews from folks here.
Pellets - Research is your friend. Buy a gun, buy pellets people say work well in that gun. Experiment. Just like reloading. Takes time to develop the right load.
It's a great sport, and once you going, costs are smaller (unless you are addicted like most people here.)
Example, I shot 120 rounds yesterday. It was $.03 per pellet, and maybe $.02 for air. Total per round cost was a nickel. Even a .22 rimfire is $.08 now with center fire cartriges going up from there. Guy next to me probably fired 100 rounds .223, so his expense was probably $.50 per round or more. I shot for under $6.00 while he shot for around $60.
Enjoy!