Between the Goko and the Kohetsu, flip a coin. I do not like the utilitarian western style handle on the Kohetsu, but based on the descriptions I have read it is a stunning amount of performance at a killer price point. The Goko is a great intro to J-knives because it is laser thin, has the wa-handle, and is a killer price, but it is a lesser steel IMHO (still good, but I love Blue#2).
The second question is more interesting. Waiting for even a modestly larger budget could really open up some options, at ~$200 there is a litany of interesting options. That said, it can be daunting because if you have never used a J-knife before, you may not know what it is you are looking for in a knife. For example, do you prefer light and thin, or mid weight and convexed, long flat sweet spot or generous belly? Buying at the entry level lets you get a feel for a knife so that when you move up the ladder you can come back and say: "love x, y, and z about knife #1, but can you recommend something that does a, b, and c better?"
Personally I would probably go the Goko route if I were in your shoes. I know that what I thought I wanted when I was starting out is not what I like today. Starting modestly will give you time to learn where to go from there. I like the Goko here because it is a bit more of a departure, stylistically from what you are used to and I think jumping further away from the edge of the pool will teach you more.
Hope this helps. Have fun!