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I’m building a small arduino project which is going to be powered using a small solar panel setup with a battery as it’s UPS for power backup during the dark.

The setup is going to be like

Solar panel->buck converter->battery charge module->battery->arduino

My question is should I buy the MPPT module or should I just use the dumb LM2596 buck converter module? Will the MPPT buck converter module help extract more juice out of the solar panel or will the other one do just fine?

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    \$\begingroup\$ Depends how sunny it is, how much power your load takes. 3W may be plenty so you can waste 30% or so in a simple converter or it may not. \$\endgroup\$ – Brian Drummond Mar 22 at 15:12
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The MPPT converter will probably have a significantly higher power draw for its own circuitry that can waste more than any gains from power tracking - even the 5-10mA quiescent current of the LM2596 might be worse than the gains over a simple low quiescent LDO.

Since in this case there is a significant voltage difference between your panel and the load (3.2V?) a switcher is almost certainly better but that might not be the case if the panel voltage matched the battery voltage better.

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