The philosophy of motorized bikes is generally to create a cheap mode of transportation that isn't really filled in well by other options. Cars are expensive, take up a lot of space, and aren't always the best option when road conditions get sketchy. Electric bikes and scooters, while falling in cost, often are still far more expensive than building a gas-powered bike yourself. Mopeds, dirt bikes, and mini bikes are often more expensive as well. Plus, most of the cheap options don't strike the same balance between road-friendly tires, lightweight construction, and the ability to add shocks and other vibration-dampening. Motorized bike kits and bicycles, in general, also allow for far more customization, as essentially, any part on the bike can be easily replaced, added to, or upgraded when desired. For example, the bike we will look at could easily be upgraded with disc brakes, a mountain bike fork for added front shocks, and a spring seat for additional dampening. Motorized bikes do often need servicing, but they can prove to be a reliable source of fun or transportation if used properly.
The Bike
The 700c Kent Rideland bicycle.
AliExpress Link
This is the first time I've personally bought a new bike with the intention of using it in a motorized bike build, and I'm really happy with most of what this bike offers. For starters, this bike is a hybrid v-style frame with regular diameter down tubes, so this should allow an engine to be mounted with stock hardware. Second, this bike employs dual v-style brakes, which are superior to coaster brakes in several ways, and leave room on the rear wheel for mounting the motor chain sprocket. It's a single-speed bike, greatly reducing complexity and decreasing the likelihood of the pedal chain falling off. Lastly, this bike is cheap and comes at just over $100 on AliExpress. You can order this bike everywhere, though, and multiple sellers on eBay, Walmart.com, and more have listings up for this bike at various prices. It also looks cool as heck and has a super eye-catching color scheme.
The Kit
One of the many motorized kits available online.
AliExpress Link
With the cheapest options, there isn't really a single kit that's worth getting over another. Despite claiming to be 80cc/100cc, most of these motors are closer to 40cc/60cc. They don't make a ton of power, but enough that they can get up to 20-30 MPH on flat ground using the 36T sprocket. Most run well enough and are fairly reliable when broken in properly. The option I linked above is listed for around $100 and includes everything to mount the motor and add appropriate controls. Again, these are listed everywhere and can be found easily for around $100 (or sometimes less).
There are many things you'll learn in the process of completing a build like this, and the end result is something you can actually ride and potentially use as transportation. It's a $200 DIY moped, and it can be done with a brand-new bike and motor for that price.
Resources
Assembly Overview
Basic Assembly Video