You might find it hard to have just 1 outfit that can do it all but for your price point the Atomic Arrowz and the TD Hyper rods are really good value. Any of the entry levels reels from Daiwa or Shimano will be fine. Personally I am a Daiwa fanboy and could recommend their stuff as I use it, I am not familiar with Shimano.
If you are going to spend $300 on a rod then I would highly recommend you go all the way to around $380 and look at a Millerods XFLC. I have a whole heap of them and they are the most versatile rod I have ever owned. The action is unparalleled. Whatever the outcome, the addiction begins with the first outfit and then you'll want a second one 😂😂😂