Hi,
I thought of a Nucleoboard, too.
But since you wrote LEDs (plural) and buttons and pmod ...
I discarded it. There is only a single LED, only a single button .. and I don´t think PMOD at all.
This all is listed in the datasheet (I assume you did read it) .. so I wonder why you have chosen it, since it does not even fit your minimal needs.
But I saw it is compatible with Arduino shield, so I struggle to understand if it is
the best fit for me (Or just overkill).
I don´t see why "Arduino compatibiltiy" should be any drawback.
What makes it compatible? The USB interface and a couple of lines to generate RESET and BOOT signal. Is there anything else?
--> Please tell why you think you don´t want it.
If I´m not mistaken this all is on the part of PCB you can break off.
Especially for testing I find it useful to have an (debug) interface to a PC. Also download compatibilty via USB (Arduino or non_Arduino) is more useful than an problem.
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There are several providers of development boards. It may depend on your region whether they are available or not.
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Thus I´d just do searchon on
* ebay
* your electronics distributor
* other reliable sources
..for according development boards.
Klaus