For standalone programming, you'll need an ISP programmer. Since you've already been using AVR with the Arduino, might as well (in my mind) stay with AVR and find a programmer to work with those. There are many offerings depending on what you want to do and what OS you want to do it on. Google "AVR ISP programmer" and see what you can find for price ranges and stuff. You should be able to find one for $20 - $40. Some folks are actually using an Arduino and made ISP programmers with them too.
If you are on Windows, it's hard to beat AVR Studio which is a free download from Atmel. You can edit, debug, simulate (same thing?) and program your chip directly from the one package, but you need a programmer which is compatible with it and many aren't, so make sure you get one that will work with it if you want to go this route (something like this
). I use Linux most of the time, but I like AVR Studio so I've set up a Windows partition pretty much just for my microcontroller work. So yea, this is the route I have chosen to do just what you're considering.
If you are on Linux and want to stay that way, you can use AVRDUDE, AVRGCC, some kind of text editor and most any programmer to do it. Many do it this way and like it, but for me it was a little more tricky to put together so I got lazy and went the other route. There are also Linux applications made for working with AVR chips which work similar to AVR Studio, but they take more knowledge than I possess to set up and work (it doesn't take much for me to get above my raisin).
For Mac, I don't know what it takes, but seems like whatever works for Linux often works for Mac too. I can't offer much help with this due to ignorance.
Quick & easy:
1) Start with getting an AVR ISP programmer and download AVR Studio
, which works hand-in-hand with it).
2) "translate" some of your Arduino projects from the Arduino code into regular C to learn the language. It's similar, but different enough to be tricky at first. Maybe I'm warped, but I like learning this stuff.
3) use your programmer and program your chip with AVR Studio via the 6-pin ISP header on the Arduino rather than using the Arduino software and USB cord. This will be good practice and dead easy since you've already got an Arduino.
Once you've done this a few times, you're there! From here, you can pretty much buy any AVR chip you want *, use the datasheet to find out which pins are for the ISP programming, and use the exact same hardware and software to program them - maybe by just hooking it up with a breadboard if you want.
This advice comes from a rank newbie myself. I decided to learn how to do just this same thing a year or so ago. I have a local "guru" friend who has helped guide me through it and I recommend finding local help too if you can, but it's pretty simple so shouldn't be a problem to get to it yourself.
*Of course DIP packages are still easiest to deal with and some of the really powerful chips have 64 or 100 pins and do not have a dip package offering. But even with those, you can solder them to one of the various breakout boards made for that and be back in the saddle with header pins. All that power in the palm of your hand. Oh the humanity!