Pretty much all aluminum gutters are the "K" style if they are not half round; you just need to know what size they are.
One thing you need to be sure of is that the existing fascia is solidly mounted and in good condition. In severe weather, the gutters need to support snow and ice buildup, and I have seen many houses have their fascia and gutters torn down by ice.
Last year I replaced all of my fascia boards and covered it with aluminum fascia covers before installing all new seamless aluminum gutters and gutter apron drip edge on the roof. The money I got from recycling all the old aluminum paid for about 1/4 of the cost of the new materials.
I got all the gutter materials from http://www.guttersupply.com/ and was very happy with their service.