Marcus is correct. You really need dice pools in the 14+ range and at least a 6 limit for your primary skills. Spellcasting for mages, the primary combat skill for the sammy, and so on. With three, you're going to have to build smart if you want to live. You need the three Ms: Meat, Matrix, Magic. Let me go into my recommendations for the three.
Meat: A melee Street Samurai can be a badass thing. But the Combat Axe is not. That's a ganger weapon, for someone who wants big and intimidating. You want big and intimidating, but you also want to actually be effective? You want a Claymore from Run and Gun, with a Personalized Grip mod, so you have a weapon that is Acc 6, Reach 2, (STR+5)P DV, -5 AP. The 14R availability is a stumbling block, unless you want to drop restricted gear on it. But 4600 nuyen (4500 for the sword, 100 for the mod) isn't too much for a runner to pull together if you want that to be your first 'in game' purchase. Until then, you want to be using a Polearm for your two-handed melee intimidation needs. Now, if you're going for the light, quick melee sammy, then the katana and a plethora of small blades is always a damn good option. Sure, it is cliche, but that's because it works. Now, even a sammy that majors in melee should at least minor in a ranged weapon of some sort. Why? Because melee only works in melee, and sometimes you can't get from where you are to where the other guy is without either setting off alarms or getting full of lead.The two ranged weapon skills I'd take a long, hard look at if I was making a STR-focused melee sammy would be Archery and Throwing. Both do damage off your STR, which is a big bonus for you. They fire slower than an automatic, sure, but they're quiet, which makes for a good way to do takedowns from a distance without letting the whole world know where you are.
Matrix: You need to have someone who can handle your Matrix needs. Dice pools of 12-14 across the Cracking and Electronics groups are a must, as a bare minimum. Always be looking for ways to exploit your skills, but watch your OS. Don't play a technomancer unless you're doing it as a pet class with the sprites, because they got royally shafted this edition, and just can't compete. Decide whether you want to be the brute force hacker or the sneaky hacker, and gear for it, but don't specialize so far you can't switch modes if you have to. Make sure you have some kind of weapon skill (I'd go with either pistols or longarms, myself) for those times when you can't just hack your way out of trouble.
Magic: A mage lives or dies by their spells. Now, you can get by with only 5 spells, but they'd better be the RIGHT spells. Two combat spells (one direct and one indirect), Heal (if I have to explain why, you need to turn in your dice), Increase Reflexes (because this makes you able to do more), and some kind of battlefield control. Illusions like Opium Den are always a winner as they provide a flat area debuff to everyone who is in the area, or manipulations like Shadow or Ice Sheet can make getting around difficult for the enemy. Or you could do some badass things with Trid Phantasm if you're clever. Physical Barrier is always good for throwing up a temporary roadblock to keep people from following you. Or you can go the other way and get some of the mindbender spells like Mind Probe or Control Thoughts.