Most invoices you receive will have a tear-off portion that you
send back to the vendor with your payment. If the invoice
doesn't have a tear-off portion, then you could make a photocopy
of the entire invoice to send with your payment. Either way,
write the invoice number on the check.
Maybe you're putting the cart before the horse here. If you want
more accountability over purchases, rather than payables, then
maybe you want to implement a purchase order system. You can
look in almost any Accounting 101 book for ways to implement a
purchase order system, or ask google. But purchase orders are a
lot of extra work, both for you and for your vendors. Some
vendors will gladly accept purchase orders, some vendors will
accept purchase orders but add handling surcharges to your
invoice, and some vendors will not accept purchase orders at all.