When should I start a trans-munar or trans-minmus injection burn?

I've completed a few successful missions to Minmus, and have always had more than enough fuel to return safely to Kerbin; however, I feel that I could perform the transfer burns better than how I'm doing them now. While it's hard to reduce my fuel load for the upper stages, reducing the delta-v requirement dedicated to the upper stages means I can afford to spend it earlier, meaning I can shed some fuel from my lower stages. My current rocket design has a bit of a weight problem, so if I can cut just 2000 units of fuel, that would be great.

So, if using a Hohmann type transfer orbit, when should I start the burn in order to reduce the overall delta-v requirement (assuming my inclination is correct and that I initially orbit Kerbin at around 125km) for both Mun and Minmus? Should I even bother with trying a low energy transfer, utilizing Mun to get to Minmus?

Should I even bother with trying a low energy transfer, utilizing Mun to get to Minmus?

No. Minimus has an eccentric orbit. Attempting to gain a gravity assist from the Mun that will provide the exact normal/antinormal force to end up in a good Minmus encounter at the exact right point of it's orbit will require some very exact calculations.

The most efficient way I know of is to match the orbital inclination before making the injection burn. From a parking orbit of approximately 100km this just happens to be as it rises over Kerbin.

I know this is an old Q & A, but I did want to point out a more efficient way than changing your orbital inclination to match Minimus.

The most efficient way to reach Minimus is to arrange your arrival with Minimus such that the encounter occurs at either the ascending or descending node. You will be orbiting along the ecliptic (wrt Kerbin), and Minimus will cross your plane as it approaches. Execute Minimus Injection and you're done.

When you reach Minimus SoI, you will have an inclined orbit wrt Minimus - which is ok. You can make Minimus relative orbital inclination changes very inexpensively at first encounter.