A couple comments. Yes for sure power your CB directly from the battery. A good place to pick up direct battery voltage is on the little stud at the rear of the Power Distribution Center, directly in front of the battery. That +12v stud is located under that little flip-up cover. Just attach a crimp-on ring connector & slip it under the nut that holds a few other connections onto that stud. Other sources of power can introduce noise into the CB... whine, static, etc.
A very good CB antenna mount is sold by Teraflex at | TeraFlex Suspensions
and | TeraFlex Suspensions
It's important the antenna mount have a bare metal connection to the tub. So if you were to buy the above mounts, you would need to grind most of the paint away from both the mount & tub where they touch. You also MUST grind the paint away from the bottom (!) of the hole in that mount that the antenna's mount sits in. The bottom of the antenna mount (called the 'SO-239 Coax Connector' in the below drawing) must ground (touch) the mounting bracket via that bare spot you ground away from the bottom of the mounting bracket's mounting hole. So the top of the 'SO-239 Coax Connector' must touch bare metal.
The above mount you pictured would work too but make sure it too gets a good bare metal connection to the tub. At least grind the paint away from the backside of where you drill its mounting holes so its nuts & washers can ground the mount to the tub.
A weak or missing electrical ground for the antenna mount will cause problems getting the antenna tuned properly so make sure to take your time providing it a good ground.
It is critical you get the small antenna mount assembled and installed correctly in the larger antenna mount. The small antenna mount is grounded under the bracket but it is magically not grounded above the bracket... at least it will be that way if you insert the white nylon insulating shoulder washer properly which insulates the antenna itself from ground. The antenna is not grounded, only the mount is. The small mount has insulation built into it which isn't all that noticeable but trust me, it prevents the antenna from being shorted to ground... so long as you install that white nylon shoulder washer properly.
The below shows how that type of mount must
be assembled.... with the insulating shoulder washer's position being critical to the antenna tuning up properly and working. I stress that because nearly every non-working Jeep antenna I troubleshoot for friends either is missing that insulating washer or it is in the wrong position.
Finally, tuning the antenna consists of adjusting its length so it can radiate as much signal as possible. That is called adjusting its SWR (standing wave ratio) which is actually fairly simple. The SWR meter's instructions tell you how to do it but you're basically adjusting the antenna's length until you get the lowest possible SWR indication on the SWR meter which means it is radiating as much power as possible. SWR meters can be found for under $20. Oh, to simplify tuning your antenna, just set your CB channel to '20' which is in the middle of the band. When it is tuned on channel 20, channels 1 and 40 will be at their best too. No need to tune those channels separately.
Good luck, come back if you have more questions.