Odyssey Battery

Hey yo quadsters, I have a question regarding CCA in batteries. My ATV is cold natured and it will start with my generic battery that's in it, (don't ask me now what battery I have in it cuz I'm at work,) but when I hook up an external battery storage unit (Beatit 1200Amps QDSP 1200A Peak 16500mAh 12V Portable Car Lithium Jump Starter) for quick jumps it fires so much faster.  Which by the way is a bad ass accessory to have around. I keep the battery in the quad fully charged all the time. My question to the pros is how much difference does the CCA of a battery contribute to the quicker start?  

Installed new battery was told that’s what was wrong when hit start button I hear 1 click then nothing?  Can the battery just not have enough amps to crank the starter the first time ? I trickle charged it overnight thought it was enough!

With this cold snap, I noticed yesterday that the battery on my grizzly was a little weak. even clicked a few times before I got it to start. I'm thinking of picking up a batter tender/ trickle charger so was wondering what people use to keep their ATV battery charged up. I was looking at these on amazon. They both have good reviews.

 
or this one

 
Kind of like this one because if the accessory plug

k I would like to take my one person off road go cart and turn it into a sand rail LIFT it new engine and transmission make it so you have to shift w/ a clutch and all the fun stuff a car has

Got a 04 Sportsman 500 that wasnt running- owner said it needed a stater and a new battery.  It ran rough (been sitting out in the weather for a while).  A friend and I started by adding a new battery and it would start barely with the choke and his hand over the air-filter.  I decided to install the new battery in the holder on the side.  we had it on the rack because the old on was still in the bike.  I tried to be nifty by turning the battery to put the terminals in an easier spot to get to, but forgot to reverse the cables too.  In a sentence, I reversed the positive and negative on the battery like a dummy.  When we discovered my mistake and corrected it, we turned on the bike, but the display did not light up and the key did not turn on the starter.  jumping the solenoid worked the starter, so we thought the solenoid just burned up when I reversed the pos and neg...  new solenoid and no difference.  what have I burned up?  Also, the shifter does not seem to do anything in the trans.  it slides back and forth like its stripped in the trans.  any help would be appreciated!!
I think the biggest issue right now is the electrical.