"Appropriate" is an individual decision.

So long as there is food on the table, a roof over your head, and you aren't jeopardizing any of the necessities then spend whatever you darn well please.

There are many factors you can weigh to help you make or justify a decision, and intended use plays a huge role.

But there is nothing "inappropriate" about spending whatever you want on a bike, first or not, given the above caveat.