The first thing to remember when you are leveling up is that an engineer needs supplies. Get a sewing kit, an oven and a bunch of canvas and find yourself a workshop to hang out in. Use makecontainer to make backpacks or whatever you like.
Make containers until you reach level 30. Then find yourself some gold and go back to a workshop. This is where the oven comes in, as you will be making jewelry via makejewelry.
As you get higher in level you can sell the jewelry for a profit. After you sell to the same pawn shop vendor for a while, the value of your wares will decrease. Try traveling around, and finding more than one NPC vendor that will buy your jewelry. Players will also need various things, so as an engineer it is a good idea to explore urban areas of planets to find all the best shops. Brave engineers may also risk mine shafts to find the best stuff. Be sure to spend lots of time in the library researching your skills. Also be aware that science, as well as some knowledges (equipment for example) will give bonuses both while in training and when adepted. Engineering and Science are a good mix.
Be sure to train your strength as soon as possible, as you will probably end up carrying things. Sometimes your movement points will deplete or become too low to continue. If this happens, find a place to sleep for a little and you can continue. Good luck!