Having  a small budget means you need to make effective choices (in fact I would say this is true for any budget).  When there is plenty of money available it is easy to build features that aren't necessarily needed (and users may not even want).  This is not a new idea, but I see this pattern repeated often enough that its worth noting.  And as a sanity check for times when I have a great idea and then diverge.

If there are constraints (time, money, resources) effective choices will follow. Sometimes those choices are hourly or daily, but more important is to make small decisions quickly.  Fail often, fail early.  When starting a new project its natural to brainstorm and get excited about all the possibilities (or perhaps trying to solve every problem up front).  But brainstorming is the beginning of the journey.  In fact, sometimes I exhaust myself trying to solve every scenario, or dream up more features than I can develop. The second half of the journey is converging on the idea (or editing down to its purest form). 

On Project Runway, you can clearly see when a designer had a great vision but didn't know how to edit.  The design looks heavy-handed, was over accessorized, missed the goal for the challenge, or was poorly constructed because the vision was too big. The beautiful, perfectly executed design pushes to the edge of the creative challenge and then pulls back (or edits) until the point of refinement.  This is why editing is Yin to the brainstorm Yang (Yin and Yang).   And why great products can happen with small budgets.

As Tim Gunn would advise on Project Runway, trim every loose thread, tighten every seem, get rid of the stuff that does not relate. Start your project with a vision and budget that are manageable, then edit every detail along the way until you have reached the essence of the idea. Your product will be pure and show disciplined restraint.