These guys are awesome. After work, I got to my bike to discover my back tire was completely flat. It had a slow leak, so I was able to pump it up enough to make it to their shop. I got there 10 minutes before closing and they were able to fit me in. They replaced my tube and picked all of the glass shards out of my tire. Awesome customer service and they saved me from having to do this myself in the dark and the cold.
A pair of disposable latex gloves: Not absolutely necessary, but good for keeping grease and grime off your hands during a repair. Also, nice to have in an emergency when it starts raining and the temperature drops 20 degrees and you don’t have a pair of regular gloves. Just keeping your hands dry and the wind from directly blowing on them makes a huge difference in comfort.
In addition to the Rema patches, put a new tire tube in your kit. The best method for dealing with a flat roadside is to swap out the tube and save the task of patching for later. If you’re not sure what size your tires are, it’s printed on the sidewall of the tire. This inner-tube buying guide has some photos of where to look. What brand is almost irrelevant as many tubes get manufactured in the same place, so whatever your local shop has behind the counter for under $10 will work fine. The only reason to spend more would be to save weight.
Main types of bicycles are road, mountain, commuter/comfort and fitness bikes. There are more specific types and other names for bike types within that, such as urban bikes (same as commuter bikes), cruiser bikes, dual-sport bikes, hybrid bikes, fixed-gear bikes, cyclo-cross bikes, adventure road bikes (aka all-road bikes, gravel bikes), road bikes, touring bikes and specialty bikes, like BMX.
Brakes come in a variety of designs depending on the age and style of your bike. Rim brakes offer more modulation but have less stopping power, so are more suited to riding on the roads. Disc brakes can provide huge amounts of stopping power so are best suited to off road riding, although ‘V’ rim brakes are also well suited to mountain biking. All brakes use a friction system to stop the movement of the wheel, so regular checks of the contact pads should form part of your regular cycle maintenance.