c-tec charges are about £40 and will do the job nicely they even come with a nice little cable that you leave permanently connected to the battery and then use a plug to connect to the charger cable. i have to leave my westy on charge almost permanently due it having a poncy battery.
you could pump the tyres up to 50psi or put it on stands. tbh if its only a few months then don't bother. ive never had any issues with and that is with tyres that are bigger in profile and only run at 17psi. 5 mins down the road and all is fine.
starting the car every week for 10 mins is possibly the worse thing you could do unless you go out and have a decent drive. best just clean it thoroughly, give it a decent polish/hoover etc. put a cover over it put the charger on and leave it well alone. maybe the odd check up now and then to have a look at your shiny car.
tbh these are cars, designed and tested to be used in all conditions. they are not temperamental classics, kit cars, race cars or what ever. just use it throughout the winter. maybe investing in some winter tyres is a good idea but apart from that just use it. would you put your 3/5 series or ford focusaway for the winter?