I would highly recommend Pumped Up (or even Wrestler, if it appeals to you more) Jax. IMO, Pumped Up and Wrestler are every bit as good (if not in many ways better) than Heavy Weapons. Jax has enough execution barriers even without the Rocket Cancels. That said, if you can get Summoner Quan's b2/low bat vortex down, nothing Pumped Up Jax requires should be an uncrossable barrier for you.
First of all, after you get his midscreens down, you will never have an issue learning run cancel combos again. Second of all, you do not even really need them to play Jax at a reasonably high level. As such, you will be able to level up and see noticable improvement with the character in actual games without having to learn his optimal combos first.
Myself and my fellow Jax players often remark that we have the most fun playing the game. The reason for this is that while Jax is high tier character who can compete with anyone in the game, he also does it by being "fair." And what we mean by "fair" is that while he has the tools to deal with any situation, it is going to take reads and conditioning and extensive knowledge of yourself and your opponent, both his character and his tendencies, in order to continue to win on a high level.
In effect, this will make YOU a better player at fighting games, as you will have to earn your wins through a combination of matchup knowledge and skill. You will not simply be able to win because you touched your opponent once and the Summoner vortex is stupid. At the same time, you will not feel discouraged as you would if you were playing a low tier against characters that simply leave your toolset outclassed.
So, now that the psychological aspects are out of the way, let me list Pumped Up Jax's toolkit:
Firstly, the combination of Energy Wave, Ground Pound, and Air Ground Pound gives Pumped Up Jax perhaps the most critically underrated zoning in the game. I legit believe it is possible that Pumped Up is a top 10 zoner in this game. If not, he is just outside of it.
While Energy Wave is slow to start and has a lot of recovery frames, it is plus 7 on block, delayable, and capable of anti-airing any enemy trying to make their way to you by air.
Meanwhile, Ground Pound is an unblockable that does 10% unblockable damage to your opponent if he or she remains on the ground. At only 21 frames of recovery, it is possible to bait enemies who have successfully jumped your Ground Pound into attempting to punish, only to hit them with ex Gotcha Grab, which does 22% raw damage.
Additionally, enemies anti-aired by one of your Energy Waves are guaranteed an additional 13% OTG damage by way of Ex Ground Pound, which is also guaranteed after a number of strings and specials.
Air Ground Pound is there to remind people you have it. It should be used, but cautiously, as the recovery is a whopping 44 frames.
Before I move on to Pumped Up's other tools, I would like to point out that Ground Pound (but NOT Air Ground Pound) low profiles many of the games mid projectiles.
Now, on to the tools you said you were looking for: Pressure and Defense. Most of the strings you will generally get used to using with Jax end in Plus Frames. His specials, when not plus ( Energy Wave), generally remain safe on block (although you should be wary of your opponent neutral ducking them).
11 starts with a 6 frame high and is +2 on block. This string all but dares your opponent to git gud. F21 is a 13 frame mid that covers a large distance and is +1 on block. 12 breaks the armor of any ex special under 11 frames that doesn't low profile the 1. 12 offers you Jax's best 50/50, as you can continue into 123 (ends in a low), or cancel directly out of it into Downward Dash Punch. 123 should always be canceled into something, as it is -17 on block and not very plus on hit.
Jax also has a 13 frame low starter in b3 (which in conjunction with Ex DDP also has its place in stuffing certain wakeups), and an 18 frame Overhead starter in b2.
As for his Defense, Ex Gotcha is a 7 frame high (careful for the neutral ducking!) which deals out 22% raw unbreakable damage to your opponent, and restands them with you at +3. Being 7 frames, it makes for a boss ass reversal/gap exploitation tool as well. It is -9 on block in Pumped Up, so it can be punished.
Dash Punch and Ex Dash Punch are great tools on wakeup, especially if you catch your opponent running in with their guard down. Both are -7 on block, but not punishable except in the corner due to pushback.
DDP and Ex DDP is the Overhead version of Dash Punch. This is where the midscreen and corner combos are made. This is essentially the move you want to hit your opponent with the most, and it can keep those sneaky, filthy neutral duckers in check, but be careful as it is highly unsafe on block.
I think that just about does it, at some point I have to decide whether not I am offering up my opinion of why you should play Pumped Up Jax, or writing the second guide on this website on the topic. Hopefully, it isn't too tl
r to read and helps you with your decision. Good luck.
))) I just mentionned Heavy Weapons as I knew it was the variation chosen at high level play - Tyrant. I already did a little homework on Jax, I know about his 11, f21 being plus on block, his wakeups, a good part of this tools etc (I get to see that online as well playing against him). I guess it's all into the matches and training, because the b2/low bat vortex is easy for me playing Quan Chi all the time, while EX OH Dash Punch - run cancel into f21 is a lot harder 
my other most played character is easily Jason, since I am a horror buff. I have fun with him, but I find he is just god awful against half the cast in a offline setting (looking at you JCage and Kitana). Other characters I have dabbled with include D'Vorah, Kung Jin, Mileena, Tanya, Sonya, JCage, Kano, and Takeda. I always come back to Jason and Cassie but I struggle with them. I really need to find just one character to stick with at the moment, before I make a bad habit out of this with all the other fighting games I am excited for. If any Cassie players can leave some tips that would be amazing. Anybody else in the community for any of the characters I mentioned above feel free to leave some tips too. Sorry if this is typed bad I'm using an iPad while my computer is being worked on.