Sprinklers do not distribute water evenly that is why you need to move and overlap them when watering a lawn. It also waters up so you lose more to evaporation and water hitting places you don't need it too. Tomatoes should not be overhead watered as much as possible since they are prone to fungal issues.
Is your timer and valves attached to ?
drip system, micro sprinklers, sprinkler hoses, emitters, or netafim?
If you want to make a cheap drip system. Get an old hose. Get a hose cap for the male end. You can get that at home depot. Caps sometimes comes with new hoses. Attach one end of the hose to the faucet. Lay out the hose in the garden. It looks like you planted in more or less straight rows, so lay your hose out in rows close to the plants. If your plants are spaced every two feet, then use a nail and make holes along the length of the pipe next the base of each plant. Do not make the holes too large or all the water will come out from a couple of holes in the beginning and the end will be dry. for the same reason, don't use a really long hose. You can cut and mend hoses so you can attach them to your manifold. You still can only run as many hoses as you have water pressure. Since the hose is not pressure compensating, you need to have enough pressure so you cannot make too many holes or make the holes too big.
A multi zoned watering timer will water one zone at a time
https://www.homedepot.com/p/Melnor-4-Zon ... 5yc1vZc63g
verses a single zone with multiple outlets running at the same time. Needs to have enough pressure to run all at the same time.
https://www.homedepot.com/p/Orbit-Automa ... 5yc1vZc63g
This would cost more but you can use the multizoned timer
Use a pressure reducer for a drip system with 4 zones.
It helps if your faucet is close to the lawn or garden. The longer the run, the more resistance and the lower the pressure gets.
I attach a 1/2 garden hose to one of the faucet manifold outlets and run it out to the garden. Cut any excess hose length you don't need an use a mender hose end. Attach the hose end to drip female faucet connector and then attach to 1/2 inch drip distribution tubing and run that out to the zone in your garden. How big the zone is will depend on your water pressure and how many emitters your zone can support. You can select to use micro sprinklers, emitters, or pressure compensated soakers or hydrotape. It depends on what you need. Put an end cap on the end of the 1/2 in tubing at the end of the zone.
Do the same for each zone.
Caution: emitters are interchangeable but tubing and connectors are not, you need to be committed to one system.
It is best to plan the layout. Calculate your gallons per hour. It will determine the total number of emitters and the sizes your system can accommodate.
If you want the system to be used over again, you have to decide your planting so that successive plantings use the same spacing pattern.
https://www.hunterindustries.com/sites/ ... ok_dom.pdf
For the grass, you do not need a pressure reducer unless you have very high pressure. Attach garden hose to faucet and run it out to the lawn. Attach to faucet connector and main drip distribution tubing. Layout sprinkler system. you want to use a hub and spoke pattern so run the main line down the middle of the lawn and using T connectors run distribution tubing to sprinklers on the perimeter and middle if needed. Tubing should be buried. Use riser T and flex riser at each sprinkler location. attach the proper cap or low pressure sprinkler head. This is a non compensating system so it cannot support a lot of heads. If there are more than three or four you need to add another zone. Each sprinkler should overlap the the next for best coverage.
I had a landscape company install a standard sprinkler system and timer with 6 zones. 2 zones for grass and 4 were connected to my drip system. You can install it yourself but they know how to lay it out and it is a lot of digging. The system is tied in before the house pressure reducer so it has higher pressure and the manifold has valves that I can close to reduce pressure to my drip system to keep it from bursting.
My water pressure has dropped a lot over the years and I had a plumber check it out. It turns out the neighbor's pressure is about the same so he said it is the city pressure that is low and there isn't much I can do to boost my individual pressure unless we can get the board of water supply to boost the main line. As a result my sprinkler no longer reaches. I have changed to low pressure heads and micro drippers to help compensate.