to make a starship in dreams it is as easy as get a air ballon and
stars are near as other countries; but if the starship is for your own nation you need a engine for travel very far and very fast, engines to travel in atmosphere, and the ship where the astronaut can stay, in travel.
The fastest engine i know it's one I never seen before, It's one i imagined by me, the controllated nuclear reaction rocket engine in my language is "el motor de reaccion nuclear controlada a reaccion"
One engine who like a rocket make's a controlated reaction, the objective of the controllated reaction it's gain speed so slowly and in enough time to make the most confortable for passengers if not it can be nefast if not takes enough time you can break the starship, etc.. The reaction must be controllated with graphene to control the reaction for enough time. At least so much time to get the most close to light speed if not up speed and then wait to turn on again the rocket in opposite direcction to stop the starship on destiny because in space if not decelerate you not alwais can stop the starship. It could be in bars like used in atomic centrals, depending of the travel you only need few tons. The formula to calculate is known is e=mc2 then you can calculate: how much combustible you need and the speed of the ship, and the time of the travel, etc.
this rockets can help us with other problems pushing stelar objects out of collision trajectories(asteroids, moons, comets, etc), be carefull and ask in O.N.U. before actuate.
This rockets when be used make time travelling because them can travel as fast as light if not superate if possible, and travel at this speed do time traveling. take care because is possible yor traveller could can't return to him her original time.
the second thing you need it's a starship. I think the best its de cuadracopter turbojet drone I'm very proud of that too
To understand, is a cuadracopter drone for people transport with " turbojet engines"
turbojet engines can be for a cuadracopter transport with something like a pwm output controlled with somthing like an arduino and a giroscope, for electronic inyection. (you can try to do a 2 o 5 person turbojet cuadracopter for economical and fun purposes not stelar i think in your workshop) with pwm controlled inyection in at least four turbines the ship is stable as a toy drone but bigger, i recommend gasoline and kerosene not litium, gas makes co2 etc but litium is toxic and can be nefast for live. Gas kerosene engines cas easy be supersonic and litium and electric not. you can use vapor from last engine too.
When accelerate you have best results starting the supersonic turbojets to fastest as they can. When the turbojets can't gain more speed it's the time for nuclear acceleration it's best accelerate progressive because nuclear have so power to destroy the starship if accelerate so fast.
One important thing you need a protection for spacial dust, in this tipe of travel a little particle can be nefast imagine a asteroid, well you need laser cutter leds makin automatized movements to melt asteroids. a sistem to protect the starship if the laser have enough power will be with 5 10 lasers making the movements of old tv's its from left to right and then down 600 lines. and melt asteroids. you can do with magnets if laser have magnetic orientation or with cnc moving to clean your way. Melt asteroids can pass trough the turbojets engines to gain acceleration.
Sorry but for ecologism but if you do this tipe of starships but is so contaminant and probably is prohibited in your nation, planet, etc but I think we can make few experiments contaminating the minimum we can for interestelar cientifical investigation purposes. Ask to onu and government.
For this reason you can make other engine artifact nuclear too, one engine who like in nuclear centrals do, but for travel, In centrals have a nuclear chamber where you hot hard water, and this hot hard water hot's the water of the water deposit how makes clean water vapor who will be expuled for the rocket output this vapor is so hot and can put the spaceship in space way to the destiny. This engnine if i can be called "Cafetera espacial" "spacial coffe machine" It wil be stronger and slower than first but, could be used for planes cuadraplanes(cuadraplanes are mix of cuadracopter and plane it means two planes surfaces in each side with turbojets in extrems, and two engines in the bottom for propulsion) and orbitational purposes, in planes vapor can move fans. It's nuclear but not contaminate the air or water with co co2 etc and not consume o2
Cheers and good luck, with invest and travels.
P.D.If you do one, please invite me to see your work.