Get a Navigation Computer. You can get one at most stations that sell ship parts. I think they're about 350 credits. It remembers where you've been and gives you your coordinates. Probably down the bottom left or on the right hand side panel if I remember correctly.
Up your sensors level ASAP. The scout might be a better ship at the start than the troop transport just due to it's possible sensor rating. Then make a custom Hi-Tech Drop Ship like the one above for your tier 2 ship.
Don't fight anything at first. Ever. Run away.
Don't bother with trading. This is a resource collection game. And exploration. You can carry 1 gazillion resources and half a galaxy's maps, but only a few tonnes of cargo. Go with the former.
Press "i" on plants and trees. You sometimes get a few bio resources. Think of it as petrol money. It's not much, but every bit helps. It trains your science officers as well, which gives better scans, which means less faffing about.
Smith Heavy Industries tends to pay more for resources, and you earn most of your money early on by trading resources (and scans). So if given the option, trade to them. The bonuses get pretty huge later on.
If you don't have the money for a tier 2 ship, but want more crew, ditch the crappy ship weapon and put a crew pod in its place. It's about 1000 credits. You won't be fighting in space for a while (tier 3+ ship), and it's better to run than fight until you have a decent sized crew with plenty of weapons and armour anyway.
Science officers are great. Get two of them. They do semi-stack. Better scans, more bio data, and the more they level, the better it is. Get 3-4 of them later when you have cash, to cover retirements.
Medical officers are great too. They semi-stack with each other and with medics. Get two at the start. If you've got a troop transport, even fire the vets and fill whatever room leftover with medics. Regen is your friend. Get more later, and plenty of medics.
Armour is incredibly important. Get lots, even if it's crap at the start. More cheap suits means more crew can come along. Crew are like ablative armour at the start. With cheap armour. Everyone is essentially a redshirt guest star other than you, your science officer and your medical officer. Think Kirk, Spock, McCoy. Everyone else is just window dressing. Even Scotty can go fuck himself.
My optimum load out at the start with the troop transport/scout, after some basic resource collecting and scans (the star you start near is usually easy-mode, so grab everything you can from it) is: Captain, Pilot, 2x Science, 2x Medical, Gunner, 3x Medic. Chuck in a Squad Leader and some Vets or Snipers if you have a transport and some weapons and spare money. But science and regen is your first priority.
Redshirts are never any good. If you're going to pay someone, make sure they're good at something. You're wasting crew, money and experience otherwise. Get professionals, not mooks.
When you've got a small crew, 2-3 hover platforms and a mining drill are worth their weight in gold. Opens up plenty of planets and resources to you. No more lava/water/mountain problems. Costs a bit, but earns you that money back very quickly. Some of these planets are dangerous for other reasons though.
Get a set of binoculars and/or a sensor kit. Cheap as and increases your vision range. Get a headlamp and a ground penetrating radar as well. Planets are now about 3-4 times faster to explore and find resources on. Even just binoculars speed up everything remarkably.
An (Improved) AT landing gear is worth the cash in saved repair costs and wages easily.
If you get some good armour and a decent medical team, you can grind/train them by walking through geysers. Eventually they'll get so good that they're almost insta-heal.
That's just off the top of my head. The game is a little slow at first, you have to play as a coward, but it ramps up pretty quickly. Bonuses get bigger, you can buy some weapons and armour, then you've all of a sudden got a 70 man army toting plasma rifles, laughing at lightning squid swarms as you genocide them. Don't fuck with those squid until then though. Or the robots.