Bounty hunter starts with a wolf, which is probably the best you can start with for outright combat.
Do the tutorial before anything.
Your starting Graviton Beam, 3x Tactical lasers, and harpoons will probably be fine. Your starting targets for combat should be small pirate patrols. You'll see them occasionally on the map.
In combat, try to draw out faster enemies, tag them with "r", and take down their shields. Don't bother shooting your Graviton laser at unshielded ships unless their armor is down. If the shields are down, launch harpoons one at a time finish them off.
For large, slow targets get around their shield using your phase skimmer; move sideways and activate it to out-turn them. Then target their engines until they're disabled, finish with missiles.
If you run out of missiles and there are still armored targets, head all the way down to the bottom of the map and retreat. Make sure to retreat other ships as well.
Once you've saved up enough, buy a Hound. With the additional cargo space, you can carry more loot back. I generally repeat until I have 3 hounds. Hounds aren't really made for combat, but if you can afford to fit them with Hypervelocity drivers or Heavy Maulers, they make capable skirmishers. They're incredibly vulnerable to missiles, so throw a vulcan into its small turret.
Once you've got the cargo space, H-Space over to Eos. Buy food, it should only be around 20-40 credits. You can then fly back to Corvus to sell during a shortage. That's a major source of credits and trading experience. If there's no shortage, store it in the storage section of the market; if you make multiple trips you can sell it all at once during a shortage for massive profit.
For skill builds, it depends on your playstyle. If you want to play with large fleets, don't put too many points into combat skills; those only affect you. If you want to play small fleets where you're the big damage dealer, don't bother with leadership skills. Most will agree that technology is what your should focus on first. Applied Physics should probably come first, but feel free to sprinkle points where you want. I generally bring gunnery implants to 5 to get that extra range.
That should be enough to start out with, anything else can come with their own questions.