I used regular non-perforated for a couple reasons: 1) It’s less work to use regular pipe as you don’t have to cover the holes with a fabric or sock; 2) It’s less expensive because less labor; 3) Because it is just carrying the water out I didn’t need to put gravel in the entire length of the trench, further saving time and money.
I put the surface drains where I needed them, and tied into the trunkline accordingly. If I had the mobile home on a hill and one whole side had water coming down under the entire homes I definitely would have used perforated and then just backfilled with gravel similar to what @Greg mentioned, but that was overkill for my situation. I just had standing water like you did that during a heavy rain was getting under the homes.
The sewer pipe I used was this. This is the PVC adapter for the gutters. And for my surface drains I used a couple of these. I connected everything up with a bunch of wye adapters to a main trunkline sloping downhill and have not had any issues since.
Did this for two homes at the same time. For 500 feet of french drains total cost was about $1,500 including labor, from Craigslist, for both (I also pitched in connecting all the lines with primer and glue and this requires some problem solving and finesse). It was a pretty bulletproof setup, but I really needed it for one of the homes as it had a “recessed” pad - why I will never know. Pro tip: get lots of 45 and 30 degree elbows to make the wye’s work. Return the extras you don’t use.