Setting date for completion

Hi all,

My solicitor has emailed asking me to call him to discuss dates for exchange and completion. Am I right in thinking that if I pick a date close to the end of the month, my first mortgage payment will be less than if I complete early in the month, due to less interest having been accrued?

My mortgage paperwork states 'your first monthly payment is made up of interest charges from the day we release the loan to the end of the month, plus your first monthly payment'.

Am I also correct in thinking it is date of completion that the loan is released, rather than date of exchange?

Thanks for all your help!