A number of reasons may exist for starting one engine over another, but most commonly it may be one engine having a hydraulic pump while another doesn't, proximity of the engine to a power source (hydraulic or pneumatic, etc), proximity of passengers to one side of the airplane (starting engine on side that doesn't have passenger entrance door), location of ground power attachments, etc.
In most light twins (this thread probably doesn't belong in the regulatory forum), while the battery may be closer to one engine than the other, the size of the starter cables from the battery mean that there's no significant voltage drop to either engine. You're usually best alternating your starts, all else being equal.
Alternating engine starts may accomplish a number of things, depending on the aircraft and the systems. It allows an independent test of your vacum pumps. If you have dual hydraulic engine driven pumps, it may be the only time you get to see each working separately, and it may be the only time during the flight when you can evaluate pump output. If you're doing a cross generator start (using the generator on the operating engine to start the second engine), it's a good time to evaluate the first start generator under a load. Other systems may be able to be tested at that time.
If your ability to see the propeller area favors one engine over the other, so be it. But remember, you're going to be starting that other engine some time...If you can't see it for the first start, you can't see it for the second, either...so is that really a good criteria for always starting one engine over the other?
While one engine may be farther from the battery than the other, they're both negative ground, and taking their power through ground...the truth is that they're both directly adjacent to the aircraft where they're bonded and grounded...the distance from the battery doesn't make a lot of difference. Further, the size of the battery cables and starter circuitry mean that the distance isn't that critical...unless you have a very low battery.
If your aircraft flight manual directs that one engine be started over the other, or if the aircraft manufacturer has established a particular policy of starting one engine first, then go with that. Otherwise, consider alternating your starts...try a little experimentation.
Whatever you decide, use your checklists, do clear the area, and fly safe.