The best advice for the campaign is rather faction specific. Some factions are poor and need to be really aggressive - attacking from the first turn or so. I would include Shimazu and Mori in this. Other factions are sitting on gold mines, whether literally or figuratively, so can afford to invest in buildings. This includes some of the eastern ones, notably Hojo. Others have to grapple with a divided kingdom (good luck!). I think Shimazu is a good starter faction as its strategic situation is fairly uncomplicated - kick out Imagawa and then turn on Mori.

OK, but some generic advice. In the early game, you can use your Daimyo to give you an early advantage in battles. His few heavy cavalry can turn the tide of a small battle, but beware of running him into the front of spears (flank charges are good if the front is engaged). I like "balanced" early forces, with some yaris backed by some archers. Ashigaru are actually ok against cav - although cav is rare early on - and since they are fast, can act as early light cavalry, running down routers. Maybe take one or two for that role. Generally, I like to move offensively on the campaign map, but fight defensively on the tactical map. Use overwhelming force to seize a province without bloodshed (the AI retreats) and try to force him to come at you, especially in a mountainous province where you can camp on a hill. Avoid attacking bridge provinces unless you have overwhelming numbers. Conversely, such provinces make excellent defensive bottlenecks. Try to advance so as to minimise your frontline, but maximise the number of neighbouring provinces you could attack, forcing the AI to spread its defenses. Be aware that the strategic AI cheats, IIRC, and can sometimes react to your movements - it's annoying, but at least it means the game is challenging (harder than MTW and RTW, IMO).

In terms of building, try to find a nice province with iron to set up troop building provinces. Also look out for provinces that give bonuses for particular unit types and develop the infrastructure for them. Take note of what your faction advantages are and try to leverage them. I like to have limited troop building provinces - maybe one for archers, one for cav and one for spears. The key tech buildings to aim for are those for warrior monks - which are awesome anti-infantry infantry - and for cavalry - which are essential for hovering up routers. Beyond that always keep upgrading those provinces for armour (that's why you need the iron) and weapons etc. In terms of economic upgrades, ports and mines seem good - but only upgrade agricultural land that is described as rich or something similar. The more hungry factions may have less luxury to make such investments though.

Have fun!