I've always thought wireless keyboards were rather pointless, unless you have a huge screen media station.
I'd be very wary of "OEM" models, if you like the twiddly bits, the OEM versions can be excruciatingly basic, with nothing like the controls and driver capabilities you get on a Chinese no-name.
I doubt if Aldi have any of their wireless keyboard/mouse sets left, but it might be worth asking if you have one nearby.
The "rechargeables" can vary - some have a charging holster for the mouse (and probably ignore the keyboard, which runs a lot longer on alkalines - others just seem to be a "normal" set, supplied with NiMH and a charger (I kid you not!).
I'm running a Logitech OEM Desktop - a very limited multimedia keyboard, a 3 button mouse, and cack drivers - I'm back to CHIC next time I need a mouse, their 1410 is a dream and the driver features are FAB!
The one thing I DO like about the Logitech mouse - it NEVER SLEEPS!
Unlike some, that need a button click or wheel turn after 2 minutes, this is always ready, and yet still runs for about a month on alkalines, a bit less on NiMH 1300 (yes, it uses AA, not weedy little AAA).
The sensor/illumination is pulsed...
1500 per second (bright) while moving
100/s (dim) in "hot standby"
10/s (fast flash) after 30 seconds idle - "warn standby"
2/s (blink) - "cold standby"
It can ALWAYS respond to movement.