The Golf 1.6 FSI is a nice starter car, definitely a lot better than the grossly underpowered 1.4 units and is generally peppy for most scenarios. I typically get around 420 miles to the tank on mine with mixed driving, much more if you're constantly cruising on the motorway.
Performance wise you not going to get big gains on a non-aspirated petrol engine so I wouldn’t really waste your money on things like performance air filters or big bore exhausts (unless you like those sort of things) as it’s not going to do much. Most mods on this particular car would be cosmetic which is not entirely a bad thing as it can be quite pretty if done up right.
You can however uprate the handling since the standard Golf suspension is a bit soft for sporty driving. The 1.6 FSI uses 50mm struts so bear that in mind when choosing dampers or coilovers. Most likely you would want to do this if you plan changing on to bigger alloys wheels and trying to avoid the "tractor look".
Lights are generally the easiest to mod, interior and exterior LED conversions can give it a fresher appearance. If the interior looks a bit battered you can change certain bits such as door grab handles (tip - new ones are cheaper at the dealer than eBay!) and chrome light switches.
If you’re keen on audio then you probably want to change the standard headunit, look out for the MK6 Golf headunits (RCD or RNS 310/510) for an upgrade while maintaining OEM appearance. There are cheaper copies on eBay but they can vary in performance. Alternatively some decent aftermarket Double Din works a treat as well. Oh and by all means do try to avoid the base S models as that only have front speakers which is a bit of a nightmare to work on for the empty rears, go for SE spec or higher if you can.
Other things you can do, well it depends how much you want to spend - frontend bumper to the GT/GTI look, OEM sideskirts, colour coded rear valance, upgraded seats etc. It's a slippery slope once you start modding!