What's the most useful thing to buy from the store first?

Solution 1:

I would recommend you to get tier 1 runes until you get to summoner level 20, then as akaGrim stated, you can get the Tier 3 Runes.

These are general purpose (In the sense that they can fit any champion) tier 1 runes that will aid your way to level 30 and they are very cheap:

3 × Lesser Quintessence of Fortitude +14.6 Health (165IP each - 495IP for the set)

9 × Lesser Mark of Insight +0.53 Magic Penetration (30IP each - 270IP for the set)

or
9 × Lesser Mark of Desolation +0.93 Armor Penetration (30IP each - 270IP for the set)

9 × Lesser Seal of Clarity +0.036 mana regen / 5 sec. per level (+0.65 at champion level 18) (15IP each - 135IP for the set)

or
9 × Lesser Seal of Vitality +0.72 health per level (+12.96 at champion level 18) (30IP each - 270IP for the set)

or
9 × Lesser Seal of Shielding +0.05 magic resist per level (+0.9 at champion level 18) (30IP each - 270IP for the set)

or

A combination of the above mentioned

9 × Lesser Glyph of Focus -0.36% cooldowns (65IP each - 585IP for the set)

or

9 × Lesser Glyph of Shielding +0.08 magic resist per level (+1.44 at champion level 18) (15IP each - 135IP for the set)

or

A combination of the above mentioned

A total set of runes will cost you around 1620IP, It is quite a bit but it is worth getting, it makes a difference on early game.
Assuming you will play with a 50/50 win/loose ratio you can get your complete set of tier 1 runes in less than 30 matches.

There are also many recommended champs for beginners which are usually very IP cheap, I am talking about champions like:

Ashe, very easy to play Attack Damage Carry, 450IP

Ryze, easy/medium skill Mage, fun to play and very powerful! 450IP

Nunu, easy/medium skill Ability Power 'Tank' 450IP

There are many other cheap champions in the price range of 450-1350IP, don't hesitate to buy one if you are liking its playstyle, as you may have noticed Riot rotates the free champions every week and you might want to play a champion you liked from the previous free week on the actual.

For more information on runes and recommended champions check:
League of Legends Learning Center: Champions
League of Legends Learning Center: Runes

Solution 2:

There is no 'right' thing to buy. There are two main things you can spend your IP on, Champions and Runes.

You don't really want to spend your IP on runes before level 20 since there are multiple tiers of runes. Level 20 hasthe best and most expensive versions of the runes you can buy. Spending them earlier is a bit of a waste, and most people are still finding their champion style like the most to begin with. The cost of fully equipping a hero with max runes is about 15k IP. You can buy general purpose runes that can be used on multiple people such as mana regen yellow, armor / magic penatration reds, HP quints, etc.

Do you know what your play style is? That could help me give some ideas of what might be a champion you'd like.

Solution 3:

As new player I really suggest you to accumulate IPs and do not spend them until you reach level 20. Than you can start build your rune library and buy some champions you liked and fit well with your game style.

Until that level I suggest you to try only "free rotation" champions, maybe concentrate on 2/3 per week, depending also on how much time you can spend playing League of Legends each week.

I prefer to not suggest any runes because this is really subjective and strongly linked to the champion and role you decide to play.