I dont know how much the oil pump cost for your engine. For what you will have invested in your rebuild. a new oil pump would be a good investment. I have never rebuilt an engine without replacing the oil pump. Im not familiar with your engine. I think you will get some help here. Mike
Sorry, the only engines i have really worked on are Kubota's.
The repair manual for the M610 may have details on engine re-assembly. It may be an idea to look at getting a manual? but if you buy it just for that, ensure it does cover the engine.
If the engine has done a lot of hours, a new pump wouldn't be a bad idea, if you don't want to replace it check it for wear. The service manual will give specs for the acceptable gap between the gear and housing.
Nothing worse than wasting an expensive re-build over something so simple.