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I am not sure I understand the context of your question completely, but here are my thoughts and suggested approach:
Set up non-stock items EquipmentHire. You could even setup three Items called EquipmentHire-DryRate, EquipmentHire-DryRateFuel & EquipmentHire-WetRate
Now let your users make a Material Request for EquipmentHire (or the others). In the description they can give more details: Like Concrete Mixer - 5 Tons or whatever.
You can either give only the approver to submit the document. Or you can set up an approval workflow for the Material Request DocType.
This Material Request then gets converted to a Purchase Order that you send to the supplier
Supplier sends you invoices. You make Purchase Invoices and Pay against these invoices. If you have to make advance payments, you can pay against Purchase Orders
I am not sure what you mean when you say receipt these payments. If you mean, mail out a receipt to your Supplier, you can use the Notifications feature to ensure that the E-Mail with the Payment information is automatically emailed to your supplier.