Since all bows/greatbows are held with 2 hands, you should realise that you can handle bows with more str req, than your str stat. Also, crossbows generally need high str low dex, which might also be in your favor.

Consider using some of these:
Dragonslayer Greatbow
Twin-Headed Greatbow

Dragonrider Bow (Higher str scaling)
Bow of Want (FTH scaling)
Short bow (lowest DEX req.)

any of the non-shulva crossbows (they scale with dark)

All the other bows tend to require higher dex investment and usually have better dex scaling than str scaling. If you intend to only use this for PvE, any bow will do. If you intend to use poison you should invest more in dex/adp to increase your poison bonus.

Looking for a bow specificly to use poison arrows that wont way me down any. Not particularly interested in its damage output although it doesnt hurt. Just need lightwieght, long range, and fast rate of fire. Just a tool to cheese annoying enemies. :P

Sea Bow is 16 str 15 dex with a C scaling in both as well as the very long range and 2 units of weight. If I infuse it with lightning, it is C str, B fth. Would that not be a decent choice? I am not too experienced with bows.

Considering you're a str/fth build, and your choice of arrows, I'd suggest just using the sea bow for its range, and the fact that you won't need any more dex investment. The damage and scaling of the bow are irrevalent if you're going to rely on poison for damage. With those in mind, a standard bow with the longest range, in my opinion, would be the most useful.

If you are only going for a bow for posion arrows its own damage is not really something to consider, its stamnia drain are what is important. So I should go with a shortbow, dragonrider bow, bow of want or hunters blackbow.

sea bow if your interest is poison, its range makes a difference.