Your options depend on your preferences and intended distance or time, among other variables. I often use my Inov8 All Terrain pro vest, which came with two 500-mL (roughly 17 oz each) hydrapak/soft flasks with tubes. Incidentally, I logged on because I have a hydration question, but it's a somewhat different angle so I'll keep that separate.
A vest may be considered overkill for runs of around 2 hours, but that's generally when I start using mine (without the detachable rear pack unless longer duration and/or variable weather requires). Always with at least one soft flask, plus or minus the other soft flask or a more traditional bottle. I practice with carrying different fuel and gear in different pockets, even if I don't 'need' all that stuff for a particular training run. In general, I like having two hydration options (one water, one electrolyte bev) when feasible. About the tubes: I like having the bite valve positioned near my mouth, although the tubes in general do annoy at times (I get whipped on occasion, not in a fun way). I think for trail running, having the soft flasks with tubes are rather helpful, as it tends to take less focus to hydrate as compared to pulling a water bottle out, let alone putting it back. That experience may vary a bit depending on the specific vest or waist pack.
I have a very simple race belt, which I have not yet worn. I am hoping that it will be useful when I only want to carry a small bottle (maybe two?) plus a little fuel. I've seen many belts/waist packs out there that should fit the bill if your primary concern is hauling a little bit of liquid.
Handhelds... I haven't used one, save for back in the day when I occasionally carried just a bottle with me. I think I'd prefer to keep my hands truly free. Still...anybody want to donate a handheld, in the name of research? :)
For most runs less than ~1.5 hours, I can get away with not bringing any hydration with me, so long as I am well hydrated (and salted) beforehand. I also don't live in the mountains, though. :)
Happy trails.