if you think you got a very faint one about a week earlier, i would maybe count that one as about 10dpo and pick a LMP of 24 days before that.
do you plan on any ultrasounds? if you do, i would go do one when you think you around 8-10w since around that time you get the best estimates since the growth has little variation at that point. (20 week anatomy ultrasounds are notorious for misjudging gestational age!)
But since those measurements can be a week off either way, i personally would do my very best to figure it out myself and tell them right off the bat the date you like and then just use the U/S to confirm and catch anything that is way way off.
Depending on who you go to for care, they may not take your word for it unless you actually tell them you had a LMP, so i personally would pick one and stick with it unless the measurements were really off. (then they will just figure spotting threw you off or you O'd late depending on what way the measurements are off.)
i have heard way too many times around mothering.com someone being totally honest with their midwife or OB, because they were led to believe that they were not going to be fussy on dates or would take their charts, or their would have no problem if they when way late or whatever, only to change there mind later in the game or they had to transfer care and the next person saw charts and were stricter. I just mention this for those that say they to play it by ear.
i feel like it is always better to have the dates on paper that are the closest you can come up with and if they error, error just a bit to the side that mades you a bit earlier and gets you a bit more room at the end, but not too much, you dont want someone thinking you have a baby comeing too early and risking you out of options when that is not the case either.
good luck and congrats!!