Noise is pretty decently controlled on most modern DSLRs, unless you’re *really* pushing things, like masochistically shooting stop-motion evening football with little lighting, in which case you probably badly screwed by other issues as well (like attaining focus lock before the play is over) unless you’ve gone rather spendy.
Regarding OM lenses, there is an adapter to use them on Four-Thirds bodies, but it will basically be manual operation, spot metering will not necessary be accurate — and the image-stabilization of the E-510 and E-3 will not function. This last bit has caused much trolling and flaming on dpreview.
A caution, though, since kayaking was mentioned — very few are splashproofed, especially below $1000. From Olympus, the aging E-1 (which does -not- exhibit good noise characteristics at high ISO — lots of chroma noise; pair w/ 14-54mm f/2.8-3.5 perhaps, barring a sweet deal on the 12-60mm f/2.8-4) and the E-3 (which blows your budget away, body-only) are the only splashproofed DSLRs. Pentax K10D has weather-sealing, but Pentax has rather few correspondingly well-sealed lenses right now. And even beat-up Canon 1-series bodies are probably well above $1K. A rain cover of some kind may be appropriate.
