While not uncommon, starting with an MRP system and adding ERP later does present some unique challenges.  I would strongly recommend keeping two things in mind: 1) the eventual integration between MRP and finance; and, 2) the finance needs from the MRP system.  Both are important, and both require financial involvement from the start, even if manufacturing goes off on their own.

Going a little deeper on the first point, it would be wise to review your financial system options related to the manufacturing system now, as well as the available integration with these systems.  Be aware that "integration" may be used to describe anything from moving a few bits of data back and forth by a spreadsheet upload, to a full end-to-end ERP.   I would recommend that you define what you mean by integration in your requirements - for example, is it one version of truth, platform compatibility for consolidated reporting, robust auditable integration points, all of the above, or something else entirely?   You will also want to understand the value of integration for your organization - how important are benefits such audit transparency, information velocity and accuracy, and personnel efficiency, to name a few?  Given the extra work that will be required to make separate systems function in your organization, is the perceived cost benefit trade-off of delaying ERP really worth it?

As for the second point, financial requirements are often ignored when finance and manufacturing functional groups proceed separately with systems.  This is almost always a mistake.  MRP functionality usually includes sales operations support (sales orders, shipments, possibly invoices and credit management, bookings analysis) as well as inventory cost (inventory value change, inventory sub-ledger, margin analysis) and procurement management (payables, purchasing).  A significant amount of your financial input resides with your manufacturing system – a decision made in isolation usually leads to disappointing results.  Best to work together from the start for a unified solution.