1) bike (have)
2) helmet (have)
3) lock (have)
4) patch kit??
5) mini pump??
6) spare tube?? (how often do you get flats?)
7) multitool??
8) rear bag, seat bag, or panniers to carry #s 4-7 (maybe just bungee a bag on the rear rack)??
9) lights (ordered some cheap on amazon)
A patch kit isn't needed, just carry an inner tube (two if you are paranoid) of the correct size and valve type. You can patch at home later if you like, but chances are, if you get a flat, you'll want to change it and carry on as quickly as possible - that means a tube swap not a patch job.
Mini pump is good, plastic tire levers are also good (a set of three costs $2 a bike store). Check how your wheels are held on. Cheap bikes tend to use a sold through axle that needs a 15mm wrench to take on or off. Quick release take no tools, and soem mountain bikes need a 6mm or 8mm allen key (8mm is only ever used on big bad Downhill bikes, so not something you'll run into).
Multi-tool is a must. Plenty of good brands. Make sure it has: 2.5mm 3mm 4mm 5mm and 6mm allen keys, phillips and flat head screw-drivers. If you have disc brakes on your bike a Torx driver is good. Rotor bolts are the only thing on most bikes that use torx bolts, so if you have rim (normal) brakes, don't worry about it.
Zip ties. just have four or five in your bag, they are even better than duct tape to a cyclist.
I like panniers, but a simple backpack works too. All this stuff will fit into a really small space. Underseat bags can hold it all just fine (maybe not two inner tubes).
How often you get flats depends a lot on you, how you ride, the roads you ride on, and how often you check your tire pressure. I get less than one flat a year commuting. I know guys who don't check their tires and get three or four. If you are riding an mountain bike style bike, always ride above 30psi on the roads. Usually more like 40 or 50 depending on tires. Skinny tire road bikes need more pressure, 60psi or more for a sport-touring bike, 100psi for a performance bike. I'd run 80% of whatever the max on your tire says and adjust from there (more air = faster but harder ride, less air is marginally slower but more comfortable).