Thanks for the information Roady, was wondering what this 'groupset' talk was all about, can make sense of what it actually means (to an extent!).
The groupset is the drivetrain and brakes, so that's the brake/shift levers, the brakes, the derailleurs, the bottom bracket (the bearings between the cranks), the chainrings and cranks, the chain, and the cassestte of sprockets at the back wheel. Better groupsets have more gears, more precise shifting, more powerful brakes, and usually a bit less weight. There are also multiple different groupset manufacturers. The big 3 are Shimano, SRAM and Campagnolo. Campagnolo are the oldest and have a lot of Italian heritage. Their gear is expensive and requires some proprietary tools. Shimano is the most popular and widely used, because it's made in the Far East where a lot of bikes are made, and they have the cheapest groupsets available. SRAM is an American newcomer. They each have different methods for shifting. Each of the three use levers that you pull towards yourself to brake, but for shifting things vary:
Shimano: Push the brake lever to shift to a bigger sprocket/chainring, push a smaller secondary lever to shift to a smaller sprocket/chainring. You can push the brake lever further to shift two or more gears.
SRAM: A secondary lever handles both down and upshifts. Push it partway to shift up, all the way to shift down. Or vice versa, I forget.
Campagnolo: A secondary lever handles the shifts to larger sprockets, but then a button on the inside of the shifter handles the shifts to smaller sprockets. The thumb button can typically be pushed further to shift more gears, and higher numbers of gears on better groupsets. I think at times Campag shifters have allowed you to shift as many as 9 gears with one full push of the thumb button, which would be the full width of a 10 speed cassette.
Given your budget, you'll almost certainly end up with Shimano, and probably something fairly near the bottom end. Shimano's road groupsets run as follows:
Tourney - only 7 speeds at the back, crap shifters with a naff thumb button in place of the second lever. Looks a bit like Campag, performs nothing like it. Best avoided.
Claris - 8 speeds at the back, proper integrated shifters from here on up the range. Perfectly serviceable. This is the bare minimum you should be looking at.
Sora - 9 speeds at the back. Lighter than Claris, and shifts better.
Tiagra - 10 speeds at the back. I don't think this is worlds apart from Sora, apart from the extra gear.
105 - 11 speeds at the back. Shifting is improved. Cable routing for the shifters is now all done under the bar tape, which some people prefer.
Ultegra - 11 speeds. Very good shifting and lower weight. More expensive, which is a consideration for replacement parts. Used on a lot of high end bikes.
Dura-Ace - 11 speeds again. This is racing grade stuff. Super light, super effective, super expensive.
Ultegra and Dura Ace are also available with electronic shifting, but I wouldn't worry about that
As said, aim for Claris as the bare minimum, and Sora if you can get it.