The main thing is don't start with cheap systems from the internet, especially if your teeth are already sensitive. The active ingredient concentration is definitely much lower in those, but that's not the only issue. With at-home whitening, it's easy to leave the product on too long, apply it incorrectly, and then you'll burn your gums or end up with uneven results. Plus, nobody will check your enamel condition beforehand - it might turn out there are already micro-cracks under the yellow buildup, and whitening will make them worse.
At a dental clinic, the dentist will first examine your teeth, treat any cavities if needed, protect your gums with a special material, and monitor the whole process. You usually see results right away and they last longer. Yeah, it costs more, but the risk of complications is minimal. If money's tight - ask the clinic for a system for at-home use with the right concentration and detailed instructions. It'll be pricier than internet offers, but safer.
One more thing: if you keep drinking a lot of coffee and smoking, any whitening is temporary. Results can fade in a few months. So think first whether it's worth spending money if the source of the problem is going to stay.