I would say there is no such thing as rushing into strength training. Whether your goals are strength, size, power, whatever, A solid base of strength is very very important, and takes a long time to build so you should start ASAP.
HOWEVER, what you can most definitely do is rush the training itself. Starting strength training, no matter your level of experience, is a great idea, but you have to be VERY patient in order for your muscle and connective tissue size and strength, as well as your technique and work capacity, to all develop in balance and at the same time.
So here is my advice. Look up 5/3/1 and follow that from the start. Follow Jim Wendler's advice, and start with 90% of your 1rm. By starting with weights that are significantly lighter than you are capable of moving, you will give yourself time to practice the movements with good form, and will give yourself plenty of room to grow. The weights may feel light for the first few cycles, but after 4, 5, 6 months the workouts WILL start to get harder. If you are patient and put the work in at the light weights, your technique will be solid and you will be able to ride the progression for a long time. But if you let your ego get in the way and set your weights too high, the weights will get too heavy too fast and you will end up lifting with shitty technique, or not being able to make the reps. Patience is key with strength training. Just remember, it may be frustrating to take a few months/cycles to be working with light weight, but that will set you up for YEARS of gains. If you don't have patience, you will end up spinning your wheels until you learn to check your ego.
Secondly, If you are interested in building more leg size as well, Boring But Big is the way to go (it's a variation on the basic 5/3/1 protocol.) Basically, you start each workout with your strength work (5/3/1), then you do 5 sets of 10 squat/deadlifts after the heavier work. This will help you a ton. You will get in heavy work first, to help build strength, and then get a ton of volume in which will 1) help your legs grow, which will make you a better lifter, and 2) allow you to practice your technique a ton. Focus on doing that 5 x 10 with the best form you can, and just work your ass off. You do that (and eat and sleep enough), and in a year your squat and deadlift will be much, much better than they are now.
That's what I've got for you. 5/3/1, boring but big. Be patient and work hard.