How deep do you want your fly in that 6' of water and how fast do you want it to sink? Since you are targeting Kings, I'd imagine you'll want to be within 1' of the bottom.

You'll need to learn to double haul so you can punch those larger Intruders. Single hauls won't generate enough rod speed (load) to push those large flies.

My early best guess for you would be to get a standard Weight Forward (WF) floating line and then a set of sink tips of varying lengths and sinking rates. 9W 444 Cortland Classic Floating Line (WF) matched up with Rio ST's in type 3 / 6 / 8. Or a Rio Versi Tip II package that has all of the above in one package

https://pacificflyfishers.com/collections/lines-sinking-tip

https://www.amazon.com/RIO-InTouch-Versitip-Fly-Line/dp/B0160BU4XK

$50 isn't going to get you much. You'll need to at least double that for lines alone and then get some good Rio leaders.

Let me know if you need more help. Start practicing your double haul