Hmmm. Then again...
I'm a 100% fixie man meself, but I'm not convinced this is necessarily the best option for the OP. It would be ok - on a short, flat commute, pretty much any bike's going to be ok - but would it be better?
I reckon gears have their place, even on a flat, short route. You get windy days and you get days when you just don't feel too great. A low gear can be your friend. I think fixed is what you go for when you've built up to a good level of strength and fitness, not what you start out with.
The OP doesn't say where he lives, or where the bike might be left during the day - very important. Any new bike is at real risk from scrotes, and in any big city these days, a nice shiny new ss is probably top of their hit list. If you have somewhere safe to keep it, this isn't an issue.
The OP needs light. True, spec for spec the ss will be lighter - fewer bits, shorter chain etc. But a good geared bike will be lighter than a cheap ss.
If I were asked to recommend a commuting bike to a newbie, I'd suggest - assuming they know one end of a spanner from another, how an allen key works, and the difference between a flat-head and a Philips screwdriver - a good 70s/80s/90s 10 speed. You can get a perfectly good one for under £100, it'll be nice to ride and it won't get nicked. Ride that for a year, and you'll learn enough (and develop the legs) to know whether a ss will be good for you, and if so, which one/what ratio etc.
The important thing is to enjoy your riding, and gears - especially at first - can help a lot with that. There's a reason 99.5% of new bikes come with them...