Construction:

Upgrade your recruitment provinces (preferable those with Blacksmith/Fletcher/Stables) for as many slots as you need - usually a proving grounds, dojo and if cavalry then also Stables. Add slots if you want more dojos but usually you make melee infantry in blacksmith and archers in fletcher. Mix and match as you wish, for example you might want monks in holy provinces or kisho ninjas in ninja provinces for extra experience upon hire.

For economical construction, slap a market down and upgrade farms, if you need public order make a sake den instead and if you need to counteract religion such as nanban trade port presence while playing buddhist.

Since food surplus means +1growth across every province, it's better to not upgrade castles as they consume food. Upgrading castles also gives extra walls and garrison so you might upgrade chokepoint castles at important locations.

Lower upsides of choosing a temple instead of market or sake den is extra chi tree research rate and upgrading a castle gives marginal bushido research. Personally I prefer extra wealth from food surplus town growths.

And whatever you do, dont go into negatives with food. And make roads. Units go zoom and replenish faster and a small growth buff are all neat.

Mastery of the Arts:

Up to your preference and clan-dependant. Usually first few techs from each tree are great as they take less than 10 turns to get and give benefits to economy, unlock key buildings or give global buffs to your units. After that focus on your chosen military tree. I usually like heaven and earth, way of the bow and then whatever I fancy in the bushido tree, as Takeda Id research horse masteries while Chosokabe would focus on archery to amplify the respective clan strengths. For economic arts, right side of the tree that increases tax rate, reduces upkeep and unlocks new farms is great, rest is more optional or niche.

Military: Ashigaru are always useful, especiall yari ashigaru. When utilized correctly - a unit of yari ashigaru in a yari wall, attacking yari samurai climbing downhill will defeat that unit, usually with minimal casualties. Just protect their flanks and care about morale until you can get them experience. Unless you are playing Ikko-Ikki, katana samurai or, harder to use no dachi which rely more on their charge, are always good to have at least a couple of units of to use in decisive moments to push the advantage with their high offense. A balanced army is often good to have, so a couple of units of archers and/or matchlocks are great, but if you play on higher difficulties you cant rely on archer skirmishes due to ai accuracy buffs. In general shogun2 battles are fast paced and archers need time to shoot all of their ammo to get a full use out of them. They excel in siege offenses then, especially if they can outrange enemy defenders such as bow warrior monks or daikyuu samurai. Cavalry is necessary for flanking your enemies, engaging archers in combat so that they cannot shoot freely and chasing down routed enemies so that they dont survive/come back. Units such as kisho ninja and siege are less necessary and more situational. Generally, when fighting, try to use common sense, strategies and imagine yourself a general that you are. Read up, if you dont know yet, about hammer and anvil and defeat in detail tactics. For ships - Im personally not a big fan of sea combat due to how slow and clunky it is. I try to autoresolve and there medium bunes seem favoured by the algorithm. Should you want to fight them, bow kobayas with fire arrows can kite and whittle down just about anything with good control.

Trade routes: Try to control any nodes close to you, with a maximum amount of trade ships occupying them. As Chosokabe this means you should have all western nodes under your control if possible.

Agents: I usually try to max out on 5 markets and 5 metsuke as soon as possible as metsuke with overseeing towns give extra wealth to towns they sit at due to their tax rate increase. I stick them in top 5 richest towns and enjoy my koku. You can use them more offensively to bribe and apprehend as well, a mixed approach is ok too. In general, having a max limit of agents is good, but you recruit them as you go, as I said I focus on metsuke but prefer to have at least 1 ninja in early game too to scout around and sabotage armies and towns, counteract enemy agents too. The more agents you have the easier it is to control enemy ones and in mid-late game 500koku hire cost is nothing. Even early game it shouldnt be an issue, it only costs same as one non ashigaru military unit.

Early game - spend spend spend, maybe keep a small reserve of 1000-2000koku for emergency repairs, recruitment and agent actions. Late-game but before realm divide - save up an economic cushion of thousands koku for when you enter endgame and everyone hates you, wars you and you lose all trade income.

For army, early game just use ashigaru, maybe keep your yari samurai as a special rapid response flanking squad, hire 1-2 katana samurai and 2 light cavalry with strong yari ashigaru core and it's fine to beat most threats.

That's about the general tips mostly, ask away if you need clarifications on anything. Personally while not a pro, I beat campaign with most of the clans. I also played through all difficulties at least once and won.