We have an idea for a Saas app which is the first of its kind. Even after extensive research, there is just one possible competitor, and even they aren't an exact match.
It's not a question of whether we are solving a real problem since it's a solution to our own problem (scratching our own itch).
In general, is it better to have first mover advantage or be the second incumbent who learn from the first mover's costly mistakes?
First and second mover advantage are apples and oranges.
The first mover has to spend the time, effort and money to be the first to build - which means making all the mistakes, doing all of the design iteration, etc. So - first mover products are expensive to produce.
The second mover, has the advantage that the first mover did all the hard work for them, and can very quickly copy for a far less cost.
To really get the advantage of being the first mover, you need to be able to market and sell the product - either at a price high enough to create a return on the high(er) investment, or to a large enough segment of the market that you can become dominant for a longer period.
The second mover may be able to get away with selling at a lower price to a smaller segment - but also may have no choice in the matter.
In many cases - you don't choose to be first or second mover, you just build your product/company.
Also be aware that just because you're scratching your own itch (a good thing!) it doesn't mean that there's a market of other companies prepared to buy your solution as SaaS at a price that makes it worth your while. You should still do customer validation if you're building this to sell. If you're building it for yourselves, that's fine but then you shouldn't be worrying about mover advantages.