Originally Posted by monahos

The current train to DMK (until the ARL extension comes online) is not intended as an airport service - it just happens to have a station in the vicinity and does not run through tourist areas. It is slow, infrequent, unreliable, and nearly as decrepit as the trains in Myanmar.
The budget choice for DMK access is the A1 bus connecting to the BTS or MRT at Mo Chit, but not advisable for a family with luggage visiting for the first time.
Then again, 3 people with hardshell luggage will be a very tight fit in a normal Bangkok taxi whose trunk is half-filled by a LPG tank. If flying in and out of DMK, consider storing a few of your bags at the airport overnight (but don't count on it, as during peak holiday season the storage areas can be full).

Departing on Thai Smile from BKK will be a more civilized experience than Air Asia from DMK (which is still better than Thai Lion Air and its single cluster of counters...)
Air Asia's 'Premium Flex' option comes with a separate check-in counter with usually hardly any wait, but is not a good value on shorter flights (~$50 for DMK-REP).
When comparing prices, keep in mind checked bags are not free on Air Asia (~$18/44lbs), unlike Thai Smile.

As for Marriott options, their various executive residences may be a good option for a family, and come with a washer/dryer which could be useful halfway through a trip. They are unattractive from a points earning point of view, if that is a consideration.