I'd suggest that some trenching with pea gravel and perforated drain hose would be better than a collection pit in one spot.
Pits are typically for stable and impermeable surfaces that slope to a single point (like a concrete pad). You have to get the high correct and ensure it stays correct. I'd only go with a pit if you have water running across your lawn and under the house.
If water is saturating the soil and then ponding, drainage hose should deal with it. It will work all the time - not just when you have surface flooding.
Perforated drainage hose is reasonably forgiving to DIY, as long as you ensure an adequate slope along the hose to the storm-water connection.
If you have clay or fine-silt soil there is a membrane fabric to place between the hose and gravel - supposedly stops the fine sediment getting in and clogging it.