Gold income as support - Bandit giving double the minion gold would be an easy income increase that's controlled (credit to someone else in this post). Something similar to this for experience or even like the old exp mastery would be an option as an item or mastery - I don't see an issue with adding another option in the trees, though placing this mastery would be tricky. The exp quints just don't do enough to help and you can't use that as a lever for supports because of the availability. I think the obvious reason gold isn't equally available is to prevent the support role from being a "safe" scale position for late game champs to sit in and collect easy gold. I can't really think of any simple way to give supports gold generation based on skilled play though. They're rewarded for that with assist gold obviously, but as previously stated support is a role that requires a lot of underappreciated work that just isn't compensated in a personal in-game way.
Recognition of success as support - There should be some form of bonus for having a strong Kill participation as support - I think it's the most telling impact they can have. I'd even be ok with supports earning more LP for wins, or lose less with each loss, especially if it's obvious they don't main support just as a general boon to encourage players to pick up the role. Other games give additional benefits to those willing to fill scarce roles, and I found it to be an awesome model personally. I was already playing in those roles and it definitely made me feel appreciated to say the least.
Itemization
Are support items sufficiently compelling or does power progression as a support often feel worse than other roles?
Power progression is non existent as a support unless you're playing a mage or a FOTM OP champ - but I think it's the positions inherent items and the champs that can thrive in spite of having to buy them. Tanks, buffers, some high base ranged damage dealers. Supports typically only get to build 1 or 2 traditional "lane" items after the slew of "required" support items(gold gen, boots, vision, redemption, aegis, etc.), and it's often another supportive item at that (zz, FH, rylais, etc.) While these items are great items there's just no way for supports to not feel hollow with all the defensive based "required" items that nobody else wants to build. An adc doesn't want to build a team shield item. Not because team shields aren't great but because the stats on the team shield active are terrible for the adc itself. The mid/top laners have the same issue, and sometimes your jungler as well. So it falls to the support - who's basically being told that their personal itemization does not matter, and I think that's part of what creates such a dislike for the position as a whole. I can't tell you how many times I was told to buy an old version of the aegis by my ad mid/top who were against ap counterparts that wouldn't build a hexdrinker themselves - then being flamed/reported if I didn't bend to their demands. Obviously if the enemy is ap heavy I'm buying it, but when they have a single AP champ... anyways. Completely understand the worlds thought process - these are the most "impactful" items a support can have with less gold and exp. Still doesn't make it enjoyable.
Is Sightstone in the right place as a mandatory 800g first buy? Are there other adjustments to the vision game that would be good both for the >experience of playing support and the game in general?
Vision as a first purchase yes. Sightstone itself? No. I despise sightstone because of what it creates. I think the vision trinkets were a great step in increasing team vision, as well as the ward option for junglers. On the other hand, the 3 gold gen vision options just don't stack up against their active counterparts. Riot maintains that vision is a team thing - but they created items 100% unappealing to anyone except those in a support role. I think elites/pro's can appreciate the general greatness that health is, but it's a bland stat that is optimal for tanks only and its far to costly for any role except a support. Laners can't afford team utility at any point in the game (or so it seems). I understand vision vs combat stats should be an important choice to force people to make, but I think having an AD friendly vision option so my top lane riven can drop an extra ward on the map is something that should be a viable option. The same can apply to ap based champs as well. I think you should have to spend gold on vision because it's an important thing to have, but it's just really unattractive to every other role.
Pre-Game
Are supports properly served by pre-game choices (runes/masteries/summoner spells) in terms of their effectiveness?
Runes - Not much to say really. If experience gain was increased scaling runes would be more viable. That's about it.
Masteries - Bandit is a legit requirement as support, and that's fine I guess. It's an easy lever for riot to control and it does have a skill reward as well with the on hit gold. The new resolve keystone is amazing - fully expect it to be nerfed, but it's got a hidden wrinkle of skill and risk/reward in it. IE: do I spend my cc with 1 enemy in range in order to lock someone down, or do I wait to catch a bigger shield and risk something bad happening because of it? It's created a new nuance to pay attention too, and I like it a lot.
Summoners - Nothing feels too out of place. Some general ideas though - One interesting thing would be maybe having a passive summoner spell as an option. A minor permanent buff in exchange for one of your summoners might be something appealing though I imagine it would be terrible to balance. An offensive version of exhaust to buff up one or all of your team mates is something that would be awesome as well. A short term damage steroid of some sort basically, though I could see the balance issues in that already. Imagine a team wide damage boost that caused damage to your own teammates in exchange for a short term group steroid. That would be fun. There's inherent risk, and obvious reward that can still be outplayed by the enemy.
The biggest pregame choice that wasn't even mentioned is the champion selection. The moment you become support 75% of champs just became off limits. Whether it's because of their item needs, scaling, etc, that's just how it's going to be in the current system. Your expected itemization tends to only "work" with a very specific line of champs. If those change, you would see more variety at the position, but overall the meta diversity at support seems to be better than most other roles.
Champion picks create the lane. Don't think there's anything you can do about certain laning patterns without seriously upsetting power curves/spikes/etc.
Closing Statement
At the end of the day I think most people don't play support because the impact you can have is just not as big as in another role. Yes, occasionally you can carry a game as a support - just not nearly as often as from other roles - and even then it's still DEPENDENT on your team mates to succeed. I personally play 4 of out 5 positions (can't adc just not good at it). It's extremely frustrating and infuriating when I decide "hey I'll support this game instead of top/mid" and then my mid/top lanes get wrecked into oblivion and there's nothing I can do to save the game. It's even worse when I know I could have won those lanes and even the game probably if I was in that role. As a support it doesn't matter if we just dominated that lane phase because I'm supporting correctly i'm not on a champion equipped to carry a team - I have to rely on the other 4 people to play well and make the right decisions to win. I'm risking an hour/hour and a half of my life in LP that I can trust these random people to not waste my invested time. I think when people go to que up, most look at support and think "Do I really trust these other people to win this game for me?" and quite frankly most probably don't. I don't expect a single player on my team to ever be good. I go in with the expectation that I must god carry every random team I'm on or I will lose - meaning not only do I lose LP and that 40 minutes, I have to spend more time to earn it back. I'd like to say that's not how it feels but that's the truth. We're expected to want to play for the good of the team but it's all for a personal rank. So every time I que up I'm essentially gambling with the hours of my life and if I'm going to lose hours of work it better be because I was the reason and not somebody else.