Bear in mind that a blurry background is a very desirable effect in portraiture.
The slowest speed with which you can shoot hand-held is roughly the reciprocal of the focal length. So with a 28mm wide-angle you can go down to 1/30th of a second but with a 100mm tele it's only 1/100th of a second or so.
Also, you don't need to use really really small apertures - most lenses have optimum sharpness at middle aperture (f4-f11). If you're doing landscapes I'm assuming you're using a wide-angle which means that a) you have lots of DoF anyway and b) you can use a fairly slow shutter speed hand-held.
Personally I have never needed to use a tripod, it's far too bulky to justify carrying around. Of course using one can only improve the quality and they are also helpful for checking that horizons and verticals are properly aligned.
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