I am looking for a new bait casting rod an reel. I need an all around one, for every type of lure. My budget is about $160. Any suggestions?

Dobyns 734 fury, savy or Sierra 

7 foot medium heavy h20 ethos, can't help you on reel but I would use 15# mono. 7:1:1 gear ratio for reel

The new vendetta and the shimano caenan.

$160 budget can get you a "good for the money" combo, but not what most of us would consider a "quality" combo.  I have zero experience with Sports Academy's H2O rods and reels, but they get very good reviews.  A Berkley Lightning (or Lightning Shock) is a decent rod for the money.  I've got a Lightning spinning rod that is around 35-40 years old that is still in use...when I use a spinning rod.    House brand rods often offer good quality for your dollar.

Also realize that no rod is going to be good with every lure.  There will be compromises along the way.  A good all-around rod is either a MF or MHF from 6'6" to 7'3"....which rod power depending on cover and lure weight.

Another reel option is to locate a Daiwa Exceler on sale for around $60.  This will leave you a bit more money for a little better rod.  New price on a Fury at places such as TW run from $110-$120.  The Savvy another $40.  I see no use in recommending a rod to you who's price leaves you no money for a reel.

Check out rod and reel combos from such places as Academy Sports, Cabela's, BassPro, etc.  Otherwise the used market is a good place to start looking.