What I would do:
Where to go:
What is now Shanxi Province, China
Prior to going:
Train for 1 month, make sure I can do a 10km run with full kit, climb walls, etc. and am also vaccinated for measles, mumps, rubella, smallpox, cholera, and polio
Also read up on medieval Chinese, make sure I could speak basic phrases with reasonable fluency
Study up on my Confucian sayings and politics of the time period
Here is a catalog of what I'd grab:
Weaponry (6kg)
--Rifle cleaning kit (0.5kg)
--Ruger Mini-14 (3kg) -- rugged, lightweight, easy-to-clean semi-automatic carbine with scope and acceptable 200yd accuracy on a man-sized target
--160 rounds of 5.56mm ammunition (2kg) -- preferably the 55gr high velocity version, but 69gr is acceptable; both can penetrate 5mm of steel plate, thicker than most 16th century steel armors
--20 autoinjectors/syrettes loaded with potassium cyanide (0.5kg) -- for "natural" deaths
Clothing (3kg)
--black colored clothing (1.5kg) -- do not want to go in naked
--large backpack (0.5kg) -- the more rugged the better
--lightweight hard-sole mocassins (1kg) -- durability is not an issue since I can get shoes in that timeline from local sources
Protection and movement (2 kg)
--non-digital wristwatch, a topographic map of the region, handheld magnetic compass with altimeter, and binoculars (1kg)
--40 autoinjectors/syrettes loaded with streptomycin (1kg) -- to protect myself against the bubonic plague and tuberculosis
Books 'n stuff (8.5kg) - unless noted otherwise, should be in both English and Chinese
--manuals on how to efficiently smelt steel (0.5kg)
--manuals on how to find and mine coal (0.5kg) -- coal should be abundant in Shanxi
--manuals on how to manufacture shaped metal items out of simpler machine tools (0.5kg)
--book on how to maintain and manufacture bolt-action infantry weapons (1kg) -- why bolt action? easier to maintain, also eases strain on supply lines due to reduced ammo consumption; English only
--book on how to build, operate, and maintain a steam engine for locomotives or steamships (1kg) -- English only
--manual on how to lay steel rails (0.5kg) -- Chinese version included so railways themselves can spread far and wide to allow faster movement of invading armies
--book on basic civil engineering and construction materials (concrete, mortar, etc.) (1kg)
--manual of basic organic/inorganic chemical manufacturing formulae (0.5kg) -- for high explosives (nitroglycerin, TNT), chemical/incendiary weapons (e.g. napalm, mustard gas, nerve gas), and methamphetamines (for trading and motivating infantry); should be lots of feedstock via coal and coal tar byproducts; English only
--manuals on how to manufacture and operate simple rifled artillery (0.3kg) -- should be short--will likely rip the pages out of the applicable book; manufacturing in English only, the rest in Chinese for ease of training
--manuals on how to better till and farm the soil; manuals on how to make chemical fertilizers and pesticides (0.5kg); again, via coal tar byproducts
--manuals on basic geology; how to find and refine top 20 industrial minerals (0.5kg); English only
--maps of large deposits of vital 20 minerals within East Asia (0.2kg); English only
--manuals of telegraph construction and operation (0.5kg); English only
--manuals on basic 20th century battlefield medicine (0.5kg); want this in Chinese for ease of training medics
--list of all 1612 ming dynasty military/political leaders, their names, ages, rough appearances, political leanings, and ultimate fates (basically were they likely to be executed? any officials that could be saved for personal use?); English only
--list of the above, but for the Manchus; English only
--list of all 1612-1650 battles and likely outcomes (three lists together, 0.1kg); English only
pencil, notebook, eraser (0.1kg)
--list of all major weather and solar/lunar events in East Asia from 1612-1622 (0.1kg) -- this one is to establish credibility as a prophet, if necessary
--manual of medieval Chinese phrases with English translations
Misc (0.5kg)
--Basic potable water and foodstuffs (0.4kg)
--A cigarette lighter (0.1kg)
This rounds out 20kg.
No need for armor or a knife, since will likely trade for those.
The plan is to land in Shanxi and build up a network of coal/iron mines, smelters, and steel part factories. Then, slowly build up capacity and production lines for infantry weapons and rifled artillery. When the time is right, incite a rebellion (by assassinating the right local officials and using weather knowledge to paint myself as a prophet) and arm a peasant army with bolt-action weapons and said artillery, march on Beijing, utilize the pre-existent population density and social organization of Ming China to impose order upon the world with railroads, steamships, and rifled artillery.
What would you do?