The most effective way to train for martial arts is to do it daily. I assume you have forms of some sort? By practicing those forms daily, you will increase your ability to do them correctly as well as to do it longer. This will help you with the type of cardio you need to do SAMBO.
In addition, strength training does help. It's supplementary so it's OK to increase slowly, but stick with compound lifts like squats, bench press, overhead press, rows, and deadlifts. Your forearms/grip will improve as the weight goes up if you use barbells. Done correctly, you will also increase your flexibility. All the lifts I mentioned will increase your core strength, which will help with whatever martial art you do.