On rear racks I like to use the Busch + Müller Toplight Line. The Line models are supposed to make judging the distance to the bike easier for following drivers, and the light emitted is not as agressive as point source lamps like the Cateye TL-LD1100, which I also use.
My Toplight Line lamps are all hub dynamo powered, but there is also a battery version, the Busch + Müller Toplight Line Permanent LED. Caveat - the switches on Busch + Müller battery rear lamps used to be rubbish, don't know if this is still the case or not.
On a lightweight bike like the Mercury it might be worth fitting a lamp on the mudguard in order to be able to remove the rack but still have a lamp mount.
I have a Busch + Müller Secula Plus dynamo powered lamp (very small but similar diffuse lighting to the Line models) on the mudguard on my Raven Sport Tour, which just has a saddlebag and no rack. This lamp also exists in a battery version, but AAA, so less stress on the mudguard.
As I like to have 2 rear lamps, on my two rackless bikes I also have a rather ugly steel bracket attached to the metal upper mudguard bridge to take the plastic Cateye bracket for a battery-powered Cateye TL-LD1100. This bracket needs to be steel to take the weight of the AA batteries in the TL-LD1100, at first I used aluminium, which broke after a time. On my bikes with racks I mount the TL-LD1100 on the seatpost, can't do that on the rackless ones because of the saddlebag.
Like André I am a fan of the LD1100, because of the good lateral visibility they give on roundabouts and junctions and because they use standard AA batteries or rechargeables. In steady mode, rechargeable batteries last at least 15 hours at full brightness, enough for a week of commuting before I retired. They last much longer in flashing mode. So I bought three LD1100's before they were discontinued.
Unlike André I use the plastic quick-release Cateye brackets, because I swap these lamps around my various bikes as necessary. I sometimes use all 3 at the same time when towing my trailer, one on the tow bike, the other two marking the left and right edges of the rear of the trailer.