This wick watering system is very inexpensive and is commonly used in hydroponics. It is probably the least expensive route you could go and is very simple, but not really any hydroponic growers first choice.
I have used a method similar to this, but not outside. I think it would work for what you intend it for, depending on a few variables. How big are your pots? What are your crops and how much water do they require every day? What is your growing medium; how much water does it retain/how well does it drain and how well do the plants tolerate having wet feet without water circulation? What are the plants fertilization needs? Will this watering system interfere with that or conversely will you be able to auto-fertilize by adding nutrients to your reservoir? If there are a lot of animals, mosquitoes or other pests in the area you may need to find a way to keep the reservoir covered so it doesn't get over turned or infested in your absence.
In any case you want to set it up and do a test run for at least the amount of time you intend to be absent so you can make whatever modifications are necessary to keep your plants alive. When you are testing it mark the water level when you first fill it and every day after that, at the same time. Be sure you are also noting the average daily temperature and amount of sun the plants get so you can make the necessary adjustments later in the season when temps are higher and sunlight hours are longer.
It may be easier for you to implement this system by using a large tray that sits directly under the plants and feed the nylon lengths up from the reservoir into the drainage holes at the bottom of the containers to about midway up. Of course, this works better when set up at the time of potting/transplanting. I have six 1 gallon containers (each with one large plant) and have used 1 5/8" thick braided nylon rope hanging down into the water reservoir. The plants sit on a re-purposed oven rack, which in turn sits atop evenly spaced concrete blocks above the water line (the rack and blocks serve to keep the containers out of the water). The ropes reached all the way to the very bottom of the reservoir with a few extra inches to spare, in case the water became shallow in my absence. The reservoir was just an old plastic storage container that was larger than the oven rack and about 3 feet deep.
If you use plastic be sure to let it sit with water in it for at least 24 hours first and drain that water out. The purpose of this is to keep toxins from the plastic from leaching into the water and poisoning the plants. Dispose of the water into the gutter or down a drain; it's no good for watering.
I now use a different set up, but that method worked for me for a while before I was able to upgrade. As long as you don't have huge containers that get full sun and require several gallons of water a day or poorly draining soil this should work for you just fine.