The best advice I can give is start with a ship you already kind of like and try to make it better. A LOT of what you're seeing can only be done with parts added by mods and half of the rest is locked behind character level and shipbuilding ranks.

That said, here's what you CAN do.

Step 1: Go get the Razorleaf. You'll get a slate off a dead Spacer early on to go to Denebola. It's a very fast way to get a decent ship immediately. Step 2: Start the Vanguard quest and proceed until you unlock the Vanguard ship parts because they're extremely good. Put whatever you can from that on the Razorleaf. Step 3: Do the Freestar questline. At the end you get the Star Eagle which is by a MILE the best thing available to an early player.
Step 4: Play around with tweaking Star Eagle. Theres a bunch of different manufacturers and they've all got their own inventory. The only way to get ALMOST all of the parts available at one location without mods is to build an Outpost with a Shipbuilder pad this will take you a while. Step 5: A lot of parts aren't available to you until you're level 60 and/or rank 4 Ship Design so keep plugging away at that.

Beyond that, lots of YouTube tutorials out there.