The Chimera mission is quite possibly one of the most insanly difficult one's I've ever seen.
There are three things you must remember in the mission:
1. See those big disk things? One hit and you're dead.
2. See the big disk thing that's shooting out big disk things? One hit and it's basically dead.
3. You must board the Chimera.
A flare launcher (or even better, the inexpensive Dust Cloud Thingamajig) will decoy exactly one out of every three disks shot. This leaves two horrendously fast long-lasting projectiles on your bottom. You might consider using long range weapons at this time, but guided missiles have a 0% chance of hitting and heavy rockets are about a billion times too powerful.
Unless you're some sort of god you've no chance in heck of beating this thing in a shuttle; it simply doesn't have the manoueverability needed to outwit the disks. (By the way, why go for a Combat Shuttle when the wonderful Mars Explorer is available to you? Nice armor, free tractor beam, and NINE jumps of fuel. This is the best ship to start off with in FH and FF hands down.) You might be able to do it in a tricked out Mars Explorer with afterburner and plasma pods, but I tried for about a day before giving up. I recommend you go in with one of the advanced fighter models (specifically the model used by Baron Mordillo), zip in at top speed, and rip off a very short burst of plasma pods. Remember: this thing is significanly less armored than a shuttle, and will explode very easily; shoot carefully.
Missions? That one's pretty early in the game if I recall correctly; you might have to stick with cargo runs. However, do watch out for an opportunity to join a shipping company, do investigate the most north-western planet for criminal activity, and....actually it's been so long since I've played it I can't remember anymore, sorry.
As for better ships, stick with a tricked out Mars Explorer for as long as possible. It's got the cargo space and (most vitally) the range you need to do most of the missions. You won't need any other ship until you get an offer for a super-ship later on. Sorry, no Tach Fighter for you in this game, although Lars may make a cameo or two. If he does, stay faaaaar away from him when there are hostiles in the area since he's trigger happy and has the super-neem-cannon of doom.
Y'know, maybe I should write a player's guide for this....nah....