General

What does the tier list look like?

Tier Lists are a very debatable thing - its impossible to create one that is "truely accurate" or one that everyone completely agrees with. Between countries, platforms and time periods, you will find very different metas, where very different playstyles and characters find success.

It's why it's generally good for newcomers to not pay attention to the tier list as much. To gain a rough idea of the meta, though, note that:

The top tiers are regarded to be Chun li, Yun, Makoto, Dudley and Ken and (generally in that order).
The very bottom tier universally consist of Sean and Twelve. Almost every other character can be competitive when played well, however both Sean and Twelve have flaws that are hard to overcome.
The middle tier is very open. Characters like Ryu, Yang and Akuma are generally more well rounded than characters like Hugo, Necro and Q.
Even difficult matchups can be overcome by patient play. There a few that are more bias than 6:4.

Which character should I pick?

It is honestly best if you pick a character that you enjoy playing, seems cool to watch or has a design you like, regardless of playstyle. Enjoying who you play outside of gameplay will make enduring with them more enjoyable. However, I'll assume you are asking this question if you don't have a specific preferance. In this case, Ken, Ryu and Gouki are the safest bets:

Ken is a top tier, one that is very versitile, with tools for every situation, and a lot of strong options. With ken, you can play a patient poking game, a pseudo-zoning game, or a rushdown game. The ways he utilizes his super art 3 are straightforward, but very effective. Ken uses a lot of the game's fundamental mechanics or understanding his game, becuase he doesn't have any specific quirk that makes him as good as he is. He is honestly the best bet.
Gouki is generally a high tier, and also a very versitile one. Like with Ken, Gouki can be a legitimate zoner or a scary rushdown character. He's still straightforward, but is not as linear as Ken if you are looking for a more "crazy" character to play. The main downside of picking gouki is that his low life and stun means players can afford to do less mistakes and that he dies quickly, which may turn down players, as well as the fact that he has not EX moves.
Ryu is usually a middle tier, but is not bad or less viable by any means. He's still well rounded and straightforward, but while he lacks some of ken's strenghts, he is still very versitile. He has other quirks that make him interesting to pick, like his SA3 setups and incredibly high damage from an EX move.

What general advice should a beginner follow? What general strategy?

Learning takes time, and its important to develop a learning strategy to play FGs with the most excitement and effectiveness if you want to improve. He are a few, universal tips:

(if you are new to fighting games - learn some of the basic terminology, such as frame data, anti airing and poking, mixups, neutral, etc. There should be terminology guides in the internet, just look up "Fighting Game Terminology")
Learn your characters' most important normals and specials first, it can be through sitting in training mode, watching tutorials or gameplan - everyone learn differently.
Learn your basic combos - hit confirms, punishes from poke\pressure, super combos. This is pretty essential, as it gives you an idea of how your character plays and how you can use some of your normals
Don't rush and try to parry - learn to block first. Blocking is safer, even if the reward is not immidiate, its worse than parrying all the time and either getting baited or missing the parry completely. Don't mash when you don't know what to do as well - you *will* get punished a lot if you do. Blocking is great, learn to love it.
Play people who are only a bit better than you, and expect to lose many of your first matches, for a differing period of time. Losing is normal, you shouldn't blame yourself, nor the game or the opponent for it. Nobody is going to shame you for losing, and if you can learn from your losses you will only be respected. Learning from loses is exactly what pro player do.
Talk with People! the best part of FGs is the community, learning, discussing and playing together is the fun. If you play on fightcade, join the third strike servers pointed out in the room for the game.

Miscellaneous

Any useful Third Strike links I can use?

[1] Official Arcade Page
[2] Japanese Wiki
Street Fighter III: 3rd Strike Forums on Shoryuken
C-Royd Teaches 3rd Strike - In-depth 3rd Strike tutorials
The Shend's YouTube Channel - Thousands of 3rd Strike matches and miscellaneous videos
Thongboy presents 3rd Strike Basics - The seminal 3rd Strike tutorial
Street Fighter III Third Strike Frame Data - Frame data courtesy of ESN
3rd Strike Junkies Podcast - Strategy podcast
3rd Strike Resources Spreadsheet - Lots of General Tutorials, Info, Videos, and Resources, along with plenty of character specific resources
3S Sprite Viewer - Extensive Sprites/Animations for every 3S character