I did Starting Strength alongside Muay Thai.

Yeah I lift for martial arts and it helps a lot.

Just be a bit careful on how you go about it, a lot of people say that getting big will make you slow, it's not necessarily true but it can be. Suggest you read up on Strength training, power/explosive/ training and hypertrophy training. Most body-building and fitness articles focus on hypertrophy only.

Power = speed x strength. So strength training helps power and explosive training (increasing speed) helps power. In terms of a vertical jump research has shown that both are just as important, training one or the other will improve your jump height (ie power) by pretty much the same amount, but training both is even better. Strength training raises the maximum force that your muscles can exert in a contraction, speed or explosive training generally allows you to reach maximum force in a contraction more quickly.

Slow movements in the 8-12 rep range that cause hypertrophy (make your muscles bigger) are not necessarily useful. However research has shown that muscles that have been worked in hypertrophy training are more receptive to strength training.

So basically strength and explosive training will help you the most. If you want to get bigger you might do some hypertrophy type training to put on the mass, but make sure you back it up with strength and explosive training so that your power is proportionate to your size.

If you only trained for size and did medium weights in the 8-12 rep range and slow movements you would likely pack on the size, but this is where you can fall into that big = slow stereotype.

Annnnnd... now I've gone and got all technical.

I was lifting up until about a month ago and will go back to it after baby arrives.
Remember that women will typically not get big like guys from lifting heavier weights. Personally...after I added weights, I dropped another size, increased my strength, and added power to my punches and kicks. My sensei noticed the difference when holding the bags for me and asked what exercises I was doing.

Yes. I go balls to the wall 3x a week lifting. Heavy weights. I also run 3x a week, do some type of plyometic work 5x a week, and get in a day of muay thai, a day of wrestling, and a day of BJJ each week.

Internal stylist here, so I was told (in general, not me specifically) not to lift weights. I think that advice is geared towards males in a normal healthy strength range. Personally, I'm a bit behind the curve so I have to work just to bring myself up to standard. The chronic problem with my shoulders proved that to me. To make up the difference I've gone back to practicing with a sword. I deliberately got one that's heavier than a competition blade.

They say if you do lift weights, do lots of stretching to make up for the loss of flexibility. Usually we just do body weight and internal resistance exercises. (I'm not sure if 'internal resistance exercises' are a thing, but that's what I'm calling them.)

And yet there are exceptions to every rule. I have seen a few exercises that involve weights, though the weights are not actually being used for the purpose of increasing muscle.

I lift 3 times a week. I work using Jim Wendlers 5/3/1 to improve my max strength. But do alot or dynamic work to make sure that I still remain fast/explosive. So for that I make sure that every lift is done with correct technique and maximal force applied so the bar is always moving fast. Add in some jumps and med ball throws/slams you cover all the bases.

I try to live by the motto "no one ever lost anything by being too strong"