Whole house flow problem

I just bought an old(90 yrs) 2 unit house. One of the thing I have on my list to fix is inconsistent and low flow to all the water outlets. After about 10 minutes in the sink water from both hot and cold slow to a trickle. After about 5 minute flow resumes. Pressure and flow rate seem low compared to other houses ive been in. Its on city water. Incoming pipe looks like 3/4, but there is a 1/2" galv 6-8" nipple attached to that then the water meter, after the water meter is goes back to 3/4. Should this nipple be replaced asap before I delve into other possible causes?

Sounds like a low-cost idea that probably will help.

I would do it first also.