Thanx guys! I really appreciate your advice! Now I know who to come to for help especially when it comes to those IC nasties! Just out of interest, having a Bullpup MK III with level 10 armor upgarde, Generator V, level 9 Tizona Del Cid front gun, all Nomad Energy Cannons and Kraken turrents, would you think I would stand a chance in the Inner Core Systems? Just curious! Thanx once again! 
Would you stand a chance?
I can pretty much guarantee that you are going to get clobbered on your first few attempts. I don't know anyone who went into the Inner Core, solo, and thought that it was immediately easy! After that, it depends on how fast you learn (smile).
In MP, most people go into the Inner Core with wingmen (perhaps a trainer or hired escort or clan mates). In SP, it is a different game. When you go into the Inner Core by yourself, most of what you know about Freelancer Combat is not immediately helpful. The nearest friendly base is four uncharted jumps away, so your Number One Priority is to learn to survive!
The Inner Core tests your ability to evade more than any other place that you have been in Freelancer. The Bullpup MkIII is a great all-around ship, but it really stands out in the Inner Core because of those dual thrusters. Without them, you will get pounded... probably quite thoroughly until you sharpen your skills.
But we learn best by being challenged, and you will learn new techniques in the Inner Core and you will sharpen your skills. You really have no choice but to improve. Adapt or perish.
That said, my opinion is that pulse weapons (such as the Tizona del Cid) are a complete waste of a hardpoint in Freelancer. I know that some players love them, but two hits with a heavy gun drain shields as much as one hit with a pulse weapon and pulse weapons do nothing at all when the target's shields are down. In other words, half of the time the pulse weapon is useless.
There are arguments in favor of pulse weapons, and they can help you to kill weak enemies quickly, but you need every bit of power that you can muster in the Inner Core. So my advice is to use high-damage, long-range, guns and leave the Tizona del Cids at home.
Nomad guns are OK, but there are stronger Class 10 weapons in Crossfire. The PPCs (Phoenix Project Cannons) sold on Earth are pretty good, Coalition Gatling guns are strong as well. But most Dom and Ancient guns are better than the best human guns.
You can get heavy-hitting weapons by killing Ancients in Devron and hostile Doms in the Inner Core. It is not easy, but it is possible.
However, my favorite gun in the game is the Dom Ka'vash Annihilator (DKA), which you can get by killing Dom Ka'vash gunboats. The DKA is not quite as powerful as other Dom weapons, but it is the longest-range gun in the game, which works well in conjunction with the Bullpup MkIII's dual thrusters. Move fast, stay out of optimal range of enemy fire, and kill one enemy before the enemy wing can pulverize you. Let your shields regenerate and repeat.
The bottom line is that you have to find a fighting style that works best for you. Ryleous Arkane is rumored to have five arms (like Farscape's Pilot), which he uses for a cool technique for doubling the rate of fire for big guns. Spiky has a fast system and fast reflexes, so he is a master of chase-and-gun. Others prefer missiles, torpedoes, or whatever. Against AI NPC's, I prefer the Space Jousting technique that I mentioned earlier in this thread. But don't do what I do just because I do it... try different things and find techniques that work for you.
As UncleGlennie said, you have to persevere in order to succeed in the Inner Core. You won't win battles the first time that you go in. Probably not your second or third time, either. Learn to survive long enough to find a friendly base for repairs and resupply, then go back to fight and explore (and take alien weapons!).