Welcome to the forums wisemonkey
By complete system I'm assuming you want/need a source unit, speakers, sub and amp? No point in beating around the bush, but getting decent quality gear + installation will be really hard for a complete system with only $1k. If you are willing to do it yourself, you might just be able to scrape through.
Without a doubt the most important component are your front speakers. Allocate as much of your budget here as possible as this is where you will hear the most difference. Good speakers powered by a bad amp will always sound better than bad speakers powered by the greatest amp ever made. Listen to as many as you can (preferably in a car if they have a demo/customers car around) and make your decision on sound, not the brand name or its supposed features. Marketing lies, your ears don't. Ideally you'd be aiming for a set of 6.5" speakers with separate tweeters. You can buy component sets where the tweeter is integrated with the main speaker, but they are typically much worse.
Don't be fooled in to buying the top of the line source unit, you won't ever notice the difference unless the rest of your system is also top notch. Decide on what features you want/need and buy the cheapest one you can find that has said features. As long as it has a decent set of pre-outs, almost any source unit will be fine. As for iPod input, make sure you play with the interface and listen to it both through the iPod and off a CD (ideally the same song). There are some awesome iPod compatable source units and there are some dreadful ones, don't get stuck with the latter.
Same with amps, don't get talked in to something with more features than you need. 50-75 watts should be enough for most speakers, but going a little higher wouldn't hurt (particularly if you decide on getting a sub too). Again, don't pay all that much attention to brands, most of the time you couldn't hear the difference between similarly spec’d models. I was told a great analogy a few years back when I first started building my then SQ competition car. Is the 200kw made by a Holden any different to the 200kw made by a Porsche? Yes how that power is made varies, its efficiency while making that power will be different; but at the end of the day, 200kw is 200kw. Build quality varies a little, but as long as you don't buy the bargain basement gear, you’ll probably never notice it.
Subs are always a big point of contention. I first tried a 10” and then a 12” in the boot of my NA6 and wasn’t really happy with the results, it wasn’t terrible but I wanted more. I talked to a few local audio shops and was convinced to build a box into the rear parcel shelf along with an 8” sub. Have had that in for about a month now and while it isn’t what I would consider great by any means, it’s still better than even the 12” I had in the boot.
Currently I’m running 6.5” mids and 1” tweeters in the doors, the 8” sub in the parcel shelf and it’s all powered by a 4x150 amp. If you were willing install it all yourself, you could probably get away with a similar enough system for around a grand.
Lots of writing but I hope that helps.
edit: forgot! Take your own music with you when you test listen, something that you are familar with so that you know what it "should" sould like. By all means listen to whatever cd the shop has chosen, as its normally in there because it makes their stuff sound the best, but always use your own music as the final decision maker.