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.
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.
First, carbon. You already know you don’t need it for your casual weekend pursuits, because you’re not counting ounces the way a professional road racer would. But to quote an article from Velonews, “Remember that professional athletes operate in an entirely different environment than the rest of us. They are all very close to each other in terms of fitness, and they are also all very close to being the absolute best a human being can be. In short, you’re much better off upgrading your legs and dropping body fat through proper training and diet.”
On the other hand, an on-bike repair kit will be a much smarter selection of tools that you are most likely to need. You should figure out the type of screws that are fitted on your bike and the things that are most likely to go wrong on a ride. Address only these things so as not to burden yourself too much with unnecessary stuff. Moreover, there are bike repair kits used on long rides and those used on shorter rides. The longer the ride, the more tools, and spare parts you will have to bring unless you want to have a very long hike back home.
Some years ago, I used to live on my bike. Riding around daily through any weather condition was bound to quickly wear down on the bike over time. I like some of the stuff that you have in your toolkit. I would say zip ties are actually really convenient, because when something came loose you could go ahead and use those to fasten them down to keep on moving ahead until you had enough time to fix it or get it checked at a bike repair shop.
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Friction gear systems are a lot simpler to adjust, because the movement of the derailer cable can be modulated as you ride, every time you change the gear- they require less cycle maintenance. Modern index shifting systems are a little more complicated because each ‘click’ must release the exact right amount of cable to allow the derailer to move the correct distance to move the chain from one gear to another. Setting up and adjusting a derailer is not difficult and requires only basic tools, but there is a methodical procedure to follow.