Rushing a bottle or not for mid really depends on the hero matchup. 3 branches gives you the fastest bottle, but the least stats to work with. On the other hand, a null gives you a lot of last hitting power since you get 9 extra damage, and the 39 extra mana can help a bit too. If your hero can't clear waves easily at low levels, then starting with a stat item like null is probably your best bet.
I personally don't play shadow fiend so I can't comment on that.
Drums is generally an item you want to get if you need an early game boost to hp and/or mana. Generally heroes that want both of these stats will use this item the best. Ember spirit and phantom assassin are pretty good examples, although these days I usually just get a bracer. I see a lot of supports pick up the item, and I think it's awful in that scenario most of the time.
Yasha is a farming item that is almost always good to get if you plan on upgrading it at some point. The only real downside is that it offers no hp until it is upgraded, but it's a fantastic item otherwise. Think of it like a midas or a maelstrom.
Sny is basically what you upgrade yasha into if your hero doesn't use a manta well. Generally, you build it if your hero wants extra movespeed and some hp. Examples of heroes I like to build this on include lifestealer, slark, bloodseeker, and riki.
Ring of aquila is what you want to get if your hero needs mana regen, but not necessarily additional max mana. Often these heroes can use their abilities to farm faster, and mana regen will help them more in the long run. Examples include slark, terrorblade, and phantom assassin. I tend to build this instead of drum nowadays.
Boots of travel are actually fairly good if you're playing against a split push lineup: the 15 second faster cd actually makes quite a bit of difference. However, I generally dislike it as a farming item because it takes so long to pay off, and offers almost no stats in return. Sure, you move blazing fast, but I find that spending a bit more cash for a yasha or a maelstrom would make you farm just as fast and also give you more impact.
Armlet ranges from mediocre to bad if you aren't buying it on a strength hero, but you probably already knew that. However, it's truly a great item for such strength heroes though. Really, almost any strength hero can make good use of the item. It's also fantastic if the enemy has no damage over time spells. Generally people like to get it on heroes that have a way of restoring their health to mitigate the damage, but this honestly is not necessary. Armlet after blink on slardar is a great way to gain back the damage you are missing, for example. In general, you should be picking up armlet if you're playing a strength carry and you want to fight in the early game.