I can kind of depend on your garden, and what you want to do for irrigation. You can be basic, and just do a rainwater tank that has some screen filtering- and use a hose on the bottom to hose feed a smaller garden. You can get complex and go for multiple tanks, filters, and irrigation lines running through a garden if you got some slope to help you along. And a lot of fudging around in-between.

I collect rainwater. The big feed tanks get pumped into smaller jugs for distribution around the ground gardens- I tend to use ollas and leaker jugs a lot, with some hand watering there. In the kitchen garden I got rainwater tanks that are huge old coolers set up on bricks to raise them up enough- those just get a hose attachment and the containers get gravity watered from there.

I've also done line feeding, soaker hoses, hydroponics...

You need to keep you collection tank clean of debris if you want to do gravity feed into irrigation lines. They will indeed clog up if there is junk in your tank. You should prefilter, and if you want, you can add in a bottom filter too. The cleaner you keep your holding tank, the less debris to clog up whatever line system you use. You still might want to flush the system out in the fall after harvest to make sure the system is clean and ready for next years gardens.

Filtering is usually pretty easy. Screens keep out big stuff, finer screens if you tend to collect silt in your water.

How many gallons do you need in reserve (stored) at any given time? What is the difference in elevation between storage outlet and ground level to be irrigated? How far is it from storage to crops? Is this to be done at minimum cost (repurposed container, functional but unattractive) or would you rather buy new equipment that looks nice? Will you be catching roof runoff or some other source?