Frankly, I've never noticed much difference in up, down or straight eye hooks. Normally nymphs and wets and streamers will ride normally (hook point down), NOT hook point up, unless you weight them on the top of the shank (like a clouser) to flip them.
Some of it, as far as dry fly hooks and down eyes, is that it may be a carry over from tradition--- back in the olden days when silk or gut were used as leaders, trout flies were traditionally tied on down eye hooks and salmon flies were tied on upeye hooks. Upeye hooks on salmon flies were/are sometimes used with a riffling hitch (knot) tied to wake flies on the surface.
Some smaller patterns 20 and under, I like to use straight eyed hooks because it's easier to thread tippet through the eye. Others might prefer upeye hooks on tiny flies because it opens up the gap a bit more than straight or down eye hooks for easier hooking.
A possible advantage of a down eye on a dry fly is that it may help to sink the tippet a bit near the dry fly making it less visible, but as i say, I've never noticed it makes a difference. Perhaps others can speak to their experience.
As far as wire goes, manufactures are all over the place in terms of their sizes (shank length, hook gap, and wire diameters) but in general there are some advantages and disadvantages-- Some lightly dressed patterns like mayfly spinners, will float better on a light wire hook like a 3xf fine (Mustad 94833 or equivalent). The tradeoff may be that they might not be as strong--- but a convincing argument can be made that the thinner wire will penetrate deeper and easier. Standard dries are typically tied on a standard dry fly hook (like a Mustad 94840 or equivalent).
As a beginning tyer, I would recommend buying a few basic “standard” decent quality but moderately priced hooks for use on different things to cover a lot of different bases, then branch out to others as your budget and curiosity allows.
Dries, emergers, nymphs you want to ride the in the surface film. Examples would be Mustad 94840, Daiichi 1170, TMC 100 or equivalents. Although wet flies like soft hackles and flymphs and other patterns are usually tied on heavier wire, you could use these dry fly hooks for these as well. You can add a couple wraps of wire or even a bead if you want to fish these deeper.
Nymphs- a perfect bend hook tends to accept beads well, so this would be a good one to use here for both with and without beads. You can also use these with a bead for caddis pupae (a wet fly) to fish them deep. A 2xlong hook like a Mustad 9671, Daiichi 1710 or equivalent.
Streamers a 3xlong hook is great for large stonefly nymphs, buggers and muddler patterns and can also be used on dry patterns like grasshoppers (with a lot of floatation so they float a heavy hook well), It’s a pretty versatile hooks, and a (Mustad 9672, Daiichi 1720 or equivalent). If you’re just startin out, use this for feather wing streamers and bucktails too.
Other hooks down the road:
At some point you may want to add 4xlong hook for a more traditional proportions on featherwing streamers and bucktails (like a Mustad 79580, Daiichi 2220 or equivalent) especially if you fish streamers in larger sizes for trout to keep the hook gap a manageable size.
Scud hooks like a TMC 2487 (fine wire) or TMC 2457 (heavy wire) depending on the depth you want to fish. These are curved hooks 2x short with a wide gap. They’re good for caddis pupa, scuds. And the light wire hook is good for emergers.
Wet fly hooks- for stuff like Soft hackles, a hook like the Mustad 3906 or Daiichi 1550 is a classic hook, with a heavy wire to help sink it to depth. But these have a sproat bend and do not except beads as easily as other hooks. If you are just starting out, you could use dry fly hooks for these patterns.
Here's a hook chart to compare apples and oranges of hooks from different manufacturers:
Fly Hook Comparison Chart