Second the gyuto over the santoku, but of course, you should consider what chores you want to perform with the knife. I don't even own a santoku....
don't dismiss the santoku too lightly - I managed quite well - thank you - for 30+ years without one. in a desperate Xmas mood, got gifted one.
okay, it's an el-super-cheepo $20 Kitchenaid from the supermarket Gadgets rack..... 7 inch.
it's stainless, very soft, needs more frequent TLC than fits my inclination. but it's the profile of the cutting edge - specifically,,, it's almost but not quite 'flat' - that makes it so handy for many chopping / dicing tasks. I would normally get out the 10" or 8" chef knife to put that amount of 'flat' on the cutting board - but the santuko style has become one of my favs - I luv it, in fact I've bought a Wuesthof santuko 4183/17 to 'replace' it - and (sigh) now I need a custom block to hold the expanded collection . . . .
do note: there's the classic very shallow belly style (the/my preferred...) and 'designer' style santuko that are essentially a chef knife with a fat point/tip.