IMO 90% of your trigger presses should be dry fire. There are lots of home aids/tools available out there now to assist with dry fire practice too, they are inexpensive and if used properly can help you learn proper fire control. One of the most common problems is not keeping the pistol completely motionless when pressing the trigger, anticipating the shot, and not having proper follow through when resetting the trigger. Dry fire aids can help show problems and also help you correct them.
Rich is right, there are a lot of shills out there now, thousands it seems, but there is also a huge increase in quality schools as experience trained guys retire from the military and other units and start up training programs of their own. Like I said, I was fortunate to work for one of the early Pro schools, back when there was fewer than 10 in the entire USA, we trained and equipped the secret service, naval special warfare, and many others with not just our gear but our developed curriculum regarding fighting with handguns back then at SigArms Academy. As I said a few posts before, there are probably 30 or more schools/instructors I would recommend. Unfortunately, the ratio of crap to good is high on the crap side.
Regarding strong/weak side training, I've posted about this here before, but I'll repeat, that Rich is right here as well. When fighting around obstacles, vehicles, on the ground around vehicles, and so on, you may not be able to get a sight picture with your strong side, and due to the random nature of cover, may have to switch to your weaker side. Wounds as well, but you're typically going to want to switch sides fare more frequently just due to the position you are in while in cover than due to some sort of injury, but training for that is obviously good too. Being able to rapidly switch sides with both handguns and shoulder supported weapons is important, and there are a few good techniques to both switch, and shoot, from your non dominant side. IMO you should always purchase a holster for your weak side, and force yourself to do entire courses of fire, even entire courses, switching to your non dominant hand as your primary.
Regarding handguns/gear, there are so many good options out there that it's really personal preference now, there is only a couple of models I would not recommend now, the vast majority are suitable IF they are suitable for you. You will here wild stories about 100s of thousands of rounds through various models/etc, this is all BS, the majority have a service life of 20 to 40k, and having worked in businesses where millions of pistol rounds were fired every quarter, I've seen every make and type have parts failures, catastrophic failures as well, with dozens of examples of each popular type we used. So ignore any nonsense you read about one model having massively more longevity over an another, failures are random, and unpredictable, much like wounds. They do happen to every make/model, and unless you are paid to shoot, or in a unit that pays for your ammunition every day, the odds are just due to cost alone few shooters will ever push the service life of their tools.
As well, Im still around cause I saw the trouble coming and reacted to it in time. And that is even more important then poking pretty little groups in paper on the range.
Repeating myself again, but this is an important lesson learned that we can all take away from - Mindset. Mindset is far, far more important than your shooting/fighting physical skills are. The main weapon is between your ears, and the more you properly train, the more effective it will become, the physical shooting and moving part in training is just a great byproduct/bonus - this is how I've always looked at training.