Is there a routine warm-up exercise that I can do (probably at the start of the day) to ensure that I can perform in peak condition if a situation occured later on and demands immediate response (in terms of combat)? I want the exercise to be as simple and efficient as possible, preferably without equipment ('cause I don't have any).
I'm afraid the body doesn't work that way, especially if you're no longer young. You can't just exercise once in the morning and remain warmed up and flexible throughout the day.
When I was training in Taekwondo in my teen years, I would stretch frequently throughout the day. First, I would wake up in the morning, get out of bed and very quickly go through a small series of stretches lasting about 30 seconds. These stretches and movements had the most benefit. After breakfast, I would do a more complete stretching and movement routine for 15 minutes or so as I watched TV. It also warmed up my joints and muscles. As I went through my day, I would find myself doing stretches and high kicks just walking around from one room to the next. It would be completely at random, and I probably looked like a dork to most people if they saw me doing high kicks at random. I'd also stretch 15 minutes mid-day and maybe another 15-30 minutes at night before dinner, certainly before and after TKD class at night. If ever I found myself bored, waiting around, or in need of a break, I'd just do some stretches and movement.
The main thing to take from that is that you won't generally be warmed up and flexible throughout your regular day. And you'll be aware of it. You'll know what it feels like if you're feeling tight and unflexible. Stretching and moving during the day will feel like an addiction. You'll be addicted to the feeling of being warmed up and loose. By taking whatever time you have out throughout the day (10 seconds even) to stretch and move around, you can get yourself to the point where if you need to fight, you won't need more than a little bit of a warm-up to be able to do your most athletic / flexible things. And without that warm-up before a fight or an encounter of some sort, you're still probably good enough that you can at least do stuff that doesn't require great amounts of flexibility.
As you age, though, your joints may become your limiting factor. You'll need to spend much more time warming up gently. And you'll need to keep doing strength training to make sure you can handle spontaneous loads on your joints. But you'll adapt to that. You'll learn what you can do and what you can get away with if you don't warm-up first. And you'll know how to move and how to limit your techniques to stuff that won't cause your knees to give out or won't pull your groin. It's mostly about knowing your limitations. An older fighter isn't flashy and doesn't waste time with athletic techniques.
But even if you're elderly, stretching and moving around throughout the day is going to improve your physical resiliency a lot. It applies universally to people of all ages.
As for what routine to use to warm up and gain flexibility, that's entirely up to you and what you prioritize. If you rely on Taekwondo-like high kicks, then you're going to target groin flexibility a lot. So do some splits, do some leg raises, etc. If you're a grappler, you're going to want to do a lot more with the upper body, the shoulders, the elbows, the neck, the torso, wrists, etc.
There are youtube videos showing warm-ups and stretching for just about every martial art imaginable. Take from those what you find useful and make your own routine. Over time, you'll probably find the most beneficial mix of techniques for however much time you have.
I wrote an answer on a similar topic at the following link, but for maintaining flexibility in kicks as you get older:
As for equipment, you'll just need to prepare your body by continuing to do strength training and by punching / kicking a bag at minimum twice a week. And for strength training, you can get away with just doing body weight exercises. There are youtube videos showing how to do them. But the bag work is really essential if you're doing kicks or punches at all.
Hope that helps.
Well this one is not quick, but there's really no better method for preparing for a day:
Sleep well for a solid 8-10 hours.
Sleeping well requires the following actions taken seriously: Exercise, stretch, eat healthy and work ergonomically. Avoid stress, excessive screen time and alcohol before going to bed.
This way your body will be rested, healed and able to take more punishment, and your brain is much more capable to tackle any challenges coming up the following day.
Any warm-ups, stretching or exercises will lose their effect really fast and may in some cases only make you weaker (muscles being tired after strength exercise or energy reserves low after endurance training). I'd suggest you do any exercises 2-3 hours before bedtime, eat a healthy protein-rich meal within an hour after exercise and go sleep early.
DO NOT SNOOZE YOUR ALARM. EVER. Just get up!
Snoozing will only promote more snoozing and fragmented, worthless sleep.