FlyingDutchman's post is spot on, though I'd probably hold back on upgrades until I've got the Infantry, Artillery, AA and Light Armor 1936 techs, and I'll still take the first move to central planning, as events will max your interventionism and hawk. Use the Rhineland Reoccupation's -2 dissent to switch to Hjalmar Schacht and one of the espionage guys with +2 IC as well, and start your heavy duty production (tanks, HQ, ships,I recommend air too) normally. Apart from the almost-finished destroyers, submarines and cruiser, you probably won't finish anything before '36 INF kicks in, then switch all your IC to upgrade until you're up to date. Unless I'm much in error, you'll upgrade every one of your land divisions at that point. Even inf '39 won't be such a big step, and inf '36 will not be hopelessly out of date anyway.
I'd use the fifth slot to get a quick '35 MOT out to start putting those on the map ASAP. You probably prefer them over cavalry and I build both anyway.
Also note that I use 8 max tech slots but all countries including the majors have the 0.5 base research speed, so you'll get the five big techs 1-2 months earlier than I.
As Germany you can get right up to the invasion of Poland without any service period extension, if you don't go into manpower burners early on (inf, gar, and especially mil), but that 12 from enacting partial mobilization will hit you like a truck so I suggest doing it when you decide to enact the Ribbentropp-Molotov pact, as this will trigger the Danzig coup, giving you -2 dissent. You still need 2k money for every other dissent point you want to get rid of.
Edit: As to the four techs above, I'm remembering my AA and its much-improved air attack value. Better to scrub AA brigades at least for the moment and get an industrial tech.