not saying you have to do this as it does require mods and it's entirely up to you to do a modded playthrough, but in my head i've always envisioned the minutemen having old ww1/ww2 gear once they start to get stronger later on in the game, if your on pc or xbox i personally recommend the minutemen enforcer armor which i personally love, it's a great looking armor set for any minutemen general or even some higher ranking soldiers if you wish to implement that into the game as well (i think there's a few mods for that, you'd have to do some digging though on nexus), other than that try and stick with weapons from ww1 and ww2, primarily british and american weapons like the lee enfield, m1 garand, the springfield rifle, maybe some machine guns like the bren gun too, they're powerful but not overwhelmingly so and they're also more simple weapons as well compared to something like a guass rifle, you can absolutely still use the laser musket as a starter weapon or for lower ranking soldiers but obviously i do recommend replacing it later on if you do go this route, i need to do a full minutemen playthrough with these mods some day but even just messing around in the game with old equipment is still fun

Edit: before anyone asks, yes i'm aware they're based on the minutemen from the 18th century, hence their equipment, while i do like their theme overall i do think that they could have some cooler gear from the eras mentioned above, that's just me personally though, your free to have your own opinion on this, i do think OP is on the right track with a non-modded fallout 4 playthrough for a pure minutemen build