[sevric]

Hi Budget
As you are just starting out with this keep it simple. Start with a very light and thin line and for a beginner i would probably recommend something like Fireline in probably the 4LB. You need this line to be light to be able to throw the light lures required any distance which is important.
As for the leader if you are throwing lures at Whiting i personally use a short length of 14-16LB normal monofilament. The line is seldom in the water and the fish follow the lure from the rear normally so light line is simply not required. Tie this to your braid via and FG knot, learn how to tie this it will be handy for any type of fishing. If you can not do this a double Uni or albrite will do as you can cast with the knot outside the guides.
Unfortunately not many of the budget option rods are great for this however the Catana and up to their maikuro range all come in at under $100 in the Shimano range. There are a lot of entry level rods of different brands to look at under $100 just make sure it is 7 feet long or longer and rated at no more than 4 KG for Whiting.
Hope this helps. There are quite a few very experienced Whiting fisho's on this site who i am sure will chip in here shortly.