capped or non capped H1B visa stamping..

[profile1235]

I will be travelling to the US for first time.

My employer named AAA had filed a H1B visa through the capped H1b visa process( i.e, through the lottery ). My I-129 got approved recently. Now i will just have to go for my visa stamping.
 
Now recently i did get another job offer from a US non profit organization named BBB and they are also ready to file my H1B visa through the non cappped h1b visa process. Can you please answer my below mentioned questions.  

1. Should i go ahead with the non capped h1b visa process for my h1b stamping ( i.e, through comapny AAA ) or i just go ahead with the capped h1b visa stamping ( i.e, through company BBB )?
Some websites i did read that the problem with the non capped h1b visa is that i will not be able to change my job from BBB to some other commerical company? i.e, if i go ahead with the non capped h1b stamping than i wont be able to change my job to some commerical company. If i want to change than i will have to re-appply h1b visa again in the next year and than go through the h1b lottery ( i.e, through the capped h1b lottery ). Can you please confirm my understanding here?

2. Also one more thing if i am really not happy with the company AAA which has filed my capped h1b visa. So my question is now once i get my h1b visa stamped through the company AAA. Than with AAA's h1b visa same stamping  can i get the same h1b transferred to the other employer BBB and than join company BBB and start wokring there right away. Is this possible?   If thats possible, than once i join BBB after sometime if i want to change from BBB to some other commercial organization CCC than will i be able to change just with a h1b transfer or will i have to re apply the h1b visa again?  Do you see any problems in this approach?

Please people help me out with these queries.

[profile1235]

In this part of the above post there is a typo. Please refer the corrected statment.

 

1. Should i go ahead with the non capped h1b visa process for my h1b stamping ( i.e, through comapny AAA ) or i just go ahead with the non capped h1b visa stamping ( i.e, through company BBB )?

[pontevecchio]

FYI your employer has filed a H1 petition for you, not a visa.

 

1. Only you can answer that question. As regards the second part your understanding is incorrect. You have been capped once giving you a total of 6 years of H1 status with any sponsor.

 

2. One is allowed to change H1 employers.

 

Non capped H1 petition is immaterial to you since you have been capped.