Ultimately top end power comes from a combination of strength and muscle coordination (i.e., muscle recruitment patterns and mental focus). Strength training can be an important contributing component, helping develop your fast twitch (type II) muscle fibers which provide the required strength, but it will not guarantee top end power. You will also have to practice the coordination and mental focus required to produce high end power (i.e., > 1000 watts) on the bike (i.e., the specificity principle). The ability to focus and fire as many applicable muscle fibers as possible to complete a task is what often sets the pros apart from everyday riders (Martin et al. 2016).
In terms of weight training itself, form is probably far more important than weight lifted. Most will focus on the weight as it is an easy to compare metric, try to avoid this pitfall as it often leads to bad or less than ideal form (even if you avoid "outrageous" weights). Light weight does not mean less of a work out as you can make lighter weights “heavier” by focusing on explosive power/speed, which is however something that should only be done after first mastering the form which itself can take a considerable amount of time.
Squats, lunges and other such exercises need a healthy dose of glutes to be done correctly and on average cyclists have notoriously poor glute development. Its too bad as the glutes are important muscles acting as an antagonist for the hip flexors. Many cyclists suffer from chronically tight hip flexors, which can often be fixed with basic glute exercises. Glute recruitment during pedaling is also important for generating the big power you are looking for (high end power is not all quads).
Being that you are a cyclist and probably sit a lot (many of us are forced to with modern lifestyles) its probably a pretty safe bet that your glutes could probably first use some development before you even jump into things like squats. If and when you feel that you are ready for squats (also consider other exercises like lunges, both straight on and lateral lunges - another huge weakness in cyclists), I would start with very light weight and focus on form and how your hips are functioning. The body is very adaptable and can find a way to "complete" a task using poor form. This is where a good trainer is key, to ensure you are performing the task properly. I would not simply go to a gym and start squatting weights with the hope of cranking out 1600 watts on the next club sprint. This is something honed over time.
If you start with poor form you will not only train muscle imbalances, but you will also be reinforcing poor muscle coordination often associated with poor form. This in turn will result in poor functioning, which can eventually lead to injury (e.g., lower back) and a long road to recovery as now you have to fix the injury, retrain your muscle firing patterns, which is no small task in of itself, and then finally train the correct muscles and muscle firing patterns themselves. So again it would be advisable to work with some professionals to ensure you start your program properly.
Also keeping the weight light and focusing on form (e.g., can you feel your glutes working, how are your hips functioning, what is your lower back doing, when do your quads kick in, how is your knee alignment, etc) you can also master when to work in strength training into your current routine. You will likely need enough rest prior so that you can do the strength training well, you also likely need sufficient rest afterwards so that you can perform well on your next bike training session. For example killing yourself strength training in the morning followed by a interval or sprint interval training in the afternoon probably isn't always a good combo - but could be depending on your abilities and goals.
Some people can handle a high back to back workload days, while others cannot. It really depends on your fitness, genetics, age, diet, mental focus, personality... the list goes on. If you have a power meter you can measure first hand how you respond to different work out structures, allowing you to fine tune your routine. This is essentially the type of services a good coach should provide as part of the for pay service.