My advise is as you suggested, Get the project running quickly and inexpensively, then re-evaluate if it is a success - Most start-ups don't get the re-evaluate stage because of one of these
- The product does not not fill a need
- Another product beat them to it
- The money runs out before the product launches and generates revenue
- Technically the product cannot be made to work right with the chosen tools
In case 1, it won't matter what you do, in case 2 and 3, best to get it out there as soon as possible. Case 4 is rare, and even more rarely, would the correct technology have been used from the start, without falling into cases 2 or 3.
So what I suggest is "quick and dirty, delivered within budget" is better than "Perfect, over budget, over time and bust". Only you can play that balancing act of whats the right balance of Quick vs Perfect.
However I also believe the total cost is similar - by doing "Quick and Dirty" what you are really doing is not saving money, you are deferring spending it till (and if) you can afford to, i.e. Taking on technical debt. As you are in start-up m mode there is a high chance you will fail before you need to payback that debt, and you need to reduce that to a minimum. There is a risk that in the future the technical debt will wipe you out as well - but worrying about that is like worrying your parachute might not open if you jump, when the plane is on fire.....