A bit of a disclaimer, though: Runes are costly, and you'll have to put several new champions on hold no matter what you do. At level 20, you will want around 5,000 IP for runes, and you'll want another 10,000 or so more over the course of your career. On top of that, there is easily more you can blow on runes if you want some real diversity. I'm not here to explain that, though -- we can leave that one to the pros.
Buying lower-level runes
Low-level runes (below tier 3) are generally a waste. Tier 1 runes are very cheap and better than nothing, so at the very least you should fill your rune page slots with tier 1 runes until you hit level 20. Most players recommend never getting tier 2 runes at all.
Honestly, it will be a long time before you fill out your rune pages with tier 3s as they are ridiculously expensive. Tier 2s are much cheaper, so you may decide to upgrade your tier 1s to tier 2s and deal with eating a little more cost in IP over the course of your career. Tier 2s are priced low enough and give enough benefit that for casual players, so I recommend just aiming for tier 2 runes and only upgrading to tier 3 runes if you have IP to waste.
The fact of the matter is, if you get 3000+ IP, you will want to spend it on a champion for a very large portion of your LoL career. After that, you'll probably be saving for 6300 IP champions. If you can take the time out between buying champions to buy some runes instead, you have stronger willpower than most players.
The easiest runes to buy are seals and glyphs. One set of seals and glyphs will be functional for literally all of your rune pages, and you should not really need others unless Riot revamps runes (or game mechanics) in the future. These sets are flat armor seals and magic resist per level glyphs.
MR/level glyphs are extremely cheap, and you should get tier 3 versions of them when you can even if you don't get other tier 3 rune sets. I bought all nine of mine as soon as I hit level 20, which was probably a mistake in hindsight (since you don't have nine glyph slots at 20). These runes have the largest late-game impact, and even in the early game they are fairly useful. Flat MR glyphs were so badly nerfed that I can't recommend them at all.
Armor seals are very important even if you're planning on being a dedicated mid laner. They reduce auto-attack damage, which is an important part of every matchup in every lane. They also reduce physical spell damage, and most importantly, the damage from creeps and neutral monsters. If you ever intend to jungle, you must have armor seals. Some junglers can't really jungle without tier 3 armor seals and heavy investment in the defense tree. They aren't very expensive, either. When I realized I needed armor seals (they're less mandatory if you're a Dominion main), I easily bought all nine in a short span of time.
Quintessences will break your bank
Glyphs and seals were nice, but quints are no joke. Of all the things you will probably want to settle for tier 2 on, quints are it. Most decent quints cost a ton of IP. They also offer relatively large boosts in performance, which is very disappointing.
The best quints to buy if you're looking to buy only one set is movement speed quints. These are particularly useful because of the global buff to champion movement speed, though it ends up being only a point or so higher than before without boots.
Any other quints will break your bank. Armor pen, magic pen, spell vamp, gold per 10, and similar are all interesting picks, but they are all very expensive and you will need to buy more than one set for all of them except for the gold quints. You can't really run armor pen on a mage, and spell vamp on an ADC is usually worthless. Movement speed is useful on everyone, even if it really only lets you juke skillshots a little bit better.
MS quints have also had numerous sales and special offers on them. If you're planning on buying tier 3s, you might want to wait until a holiday event.
Marks are simultaneously expensive and require you to buy more than one set. There is no way around it. You will probably also want to settle for tier 2 runes here unless you're a hardcore player. Tier 3s cost over twice as much, and the benefit is relatively small.
The best marks to buy are flat penetration runes. You'll need one set for physical and one set for magical, of course. Magic pen runes are essentially mandatory; for mages, they're one of the biggest damage benefits at all levels.
Armor pen runes are still useful, but AD-based characters have more options. A single crit chance mark can randomly lead to a victorious lane. It's slightly less than 1% chance to crit, but a single lucky crit can greatly swing a game early on. It's a good investment to have one. Numerically, crit chance marks are not that great in terms of damage performance, and it's fairly easy to cap crit chance at 100% for an ADC. However, having a small chance to get a big swing can win some games on luck, so it's good to sacrifice a bit of power for that 1%.
Flat AD marks are also nice, since they are cheap and help a lot with last-hitting. Early game, they are a better benefit than armor pen (or crit chance). I recommend having at least one or two in your AD-based rune pages, and you can buy a full set if you want more power early on or if you play AD-based characters who deal magic damage with their spells, such as Tristana or Miss Fortune.
These should leave you with two rune pages, one for magic damage champions and one for physical. You don't really need more than that to be effective, though having more helps give you more build options. I'm buying expensive hybrid pen runes right now (for Elise, and to a lesser degree, Evelynn and Jax), and I'm hating every minute of it. Hopefully you guys have a better time with runes than I did.
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