You start the game with one of three ships. None of them are going to take you vary far. If you're very good and skip optional risks you can take the Wolfen Gunship through the first section of the game with basic equipment, but if you're reading this guide you're probably not that good. The EI500 Freighter is not so well equipped and the Sapphire Yacht will have trouble making it through the first system without upgrading.
There are two devices that exert an enormous effect on your choice of equipment. With the exception of the EI500 which may choose to retain its omnilaser in any case. If you can buy a cannon accelerator or laser collimator you lock yourself into using laser or kinetic weapons for the early game and possibly even the middle game. If both are available it's probably best to choose just one.
Your starting shields are not very good. The Wolfen has a hull plate ionizer, which is a level 2 shields with an advantage against kinetic weapons. You can hold onto this for a little while if you're short on cash, but if you don't have better by Rigel you may want to hold off on some of the arena fights until you upgrade. The other ships have the Class I Deflector, which is the weakest shield in the game. It will stand up to the weak foes in Eridani, but you'll want something better very soon. In Eridani you can't normally buy anything above level 3 and nothing below level 3 is worth buying so your options are pretty much limited to the Solon Shield and the Monopole Deflector. The Solon is a superior shield against everything but blast, and blast is a damage type you'll only encounter in missiles for quite a while. Unfortunately the Solon also prevents you from using lasers at all. This makes it a poor fit for the Wolfen, which has one of the better laser weapons as its starting weapon, and the EI500, which has a tendency to get maximum utility from omniweapons because of its poor maneuverability. There are no non-laser omniweapons in the early game. The hull plate ionizer can be considered a weaker version of the Monopole Deflector. Choosing the Solon will influence your weapon choices as strongly as finding a cannon accelerator and not a laser collimator, and your shield choice will also potentially influence your armor choices. Obviously if you have a laser collimator the Solon will make it useless and if you have a cannon accelerator the Solon is the perfect complement.
Armor is what keeps you alive when your shield goes down. The faster your ship the less you need. In general there are two ways to armor your ship. You can select armor that complements your shield on the assumption that you're most likely to need armor against opponents that do damage of types your shield is vulnerable to, or you can use balanced armor in recognition of the possibility you may find yourself in trouble with any type of enemy under the wrong circumstances. Armor is most important if you use the hull plate ionizer, not only because it's a weaker shield, but also because its hitpoint total is limited by the state of your armor. Titanium and plassteel armors are balanced. Ceramic armors and photo-organic armor are better against lasers. Reactive armors and polymesh armor are better against kinetic weapons. XMH armor has very good stats for its level, but cannot be easily repaired. Higher level armors are better than lower level armors in almost all cases.
As Al Capone once said you'll get more with a kind word and a gun than with a kind word alone, which is a good thing because in Transcendence a kind word gets you nothing at all. There are very few opportunities to make money that don't involve weapons and they're too limited to provide you with enough fuel to reach the edge of human space even if the Iocrym blockade were responsive to kind words. If you've found an enhancer that pushes you into one weapon type or another stick to that type. If you've got a Solon shield stick to kinetics. If you have no enhancers or the possibility of buying either enhancer you have a choice to make. Lasers travel faster, but not instantly, and have more range than most kinetics. Kinetic weapons do more damage. Outlaws generally resist laser. Pirates generally resist kinetic if they resist anything. Heliotrope Destroyers resist laser quite a lot, but are closer to midgame. The laser collimator provides a bigger boost than the cannon accelerator, making up for the damage gap.
The odd situation from pre-1.0 versions where some level 2 lasers had far higher raw damage than the level 3 turbolaser is gone. The turbolaser is substantially improved and if you are going to use lasers it is what you want to use.
For kinetic weapons the best thing you can buy in Eridani is the DK10 Arbalest Cannon. As with the turbolaser and the dual laser the AK15 Partisan Cannon may supersede the Arbalest, but since the damage per projectile is higher for kinetics the advantage will switch at a higher level than for the lasers.