"Board" and "Chip" are self-explanatory, as you say.
Generally, just leave "Timer1 Clock" set to "CPU". It's the clock source for Timer1. Doesn't affect "Clock". I've never played with this, so can't say more with confidence.
"Clock" is the speed of the processor. If using an external crystal/resonator, choose the speed to match. Otherwise, when using "Internal", it's up to you. I usually run mine at "8MHz Internal". Nice and fast, and doesn't waste pins on an external resonator. An external oscillator will give better precision, at the cost of those pins. I'm sure you already know this.
"BOD" You have it. "Brown Out Detect" pulls RST low if the voltage drops below the defined level. You can set this to avoid unwanted behaviour if the voltage is low. Handy for battery operation.
For a 5V supply, I set it to 4.3V. For a 3.3V supply, 2.7V is probably appropriate.
In most other regards, there's no difference between the cores in actual use. (Except for the voltage reference we've been discussing.)