I mean, I have two core sets, two greyjoys and one of the princes of the sun, plus refugees of war.
What should I aim for to build a nice and working Targaryen deck? I'd want to go for Burn, but then again, I'r really want it to have the dragons at the spotlight... So, which lcg exp's should I buy?

My first thought is to use a search to look at the cards and really decide which ones you 1. have to have, 2. want to have, 3. would be nice to have.

Here is a good one: http://info.wsisiz.edu.pl/~szczesnj/index.php

After writing those down, you can see which sets have the most cards you really want. I would start by looking at Targ characters, then targ events, then targ locations, then targ attachments and plots, then nuetrals (events, characters, etc.).

That is how I would do it. Good luck!

Make sure the first Chapter Pack you prioritize is Ancient Enemies.

Plot" Fury of the Dragon

Character: Dargon Thief.

Staples - trust me.

Yeah, I agree with Rings (and Stag's list of "staples"). The card pool is big enough that you have to figure out which type of deck you want to build. If you want to build "burn," then I think a shadows-heavy decklist is the way to go. If you want dragons to play a more central role in the deck, then you have a lot more flexibility. I honestly think the best way to go with a dragon-centric deck is something fast/aggro (with higher claim but generally lighter on burn), which probably means either dothraki or (possibly) a summer-themed deck. The Summer/seasonal mechanics (from the A Time of Ravens block) are often underwhelming, but Targ can take advantage of summer for the draw, and also because Fairweather Followers are amazing with Forever Burning when it is summer.

Just for more background (in case it helps), the reason shadows-based burn tends to work well is that shadows gives you draw with King's Landing, from the Secrets and Spies chapter pack, and added burn with The Dragonpit, from Tales from the Red Keep. Since Targ's draw engine can be hard to get going, shadows-based draw using King's Landing is particularly useful. (Note that despite her text, Maegi Crone really isn't a reliable draw engine, even in a burn deck, since she's so expensive to play and dies very easily.) The -1 STR effect from Dragonpit essentially means that all your -2 burn effects (Flame-Kissed, Dragon Skull, and King's Landing Assassin if you're playing it) can kill any 3-STR character, so you don't have to stack up burn effects to kill the opponent's 3-STR characters. Excluding Wildlings, most problematic characters tend to be 3-STR (Castellan of the Rock, The Red Viper, etc.), so it's nice to be able to burn those reliably/quickly using only one burn card.

If you decide to go shadows, it's a heavy investment into the King's Landing block though, as you should run at least 2x of both of those locations AND various other shadow characters from other King's Landing block chapter packs to fuel that draw/burn effect. In general, this block contains a lot of good cards for all of the houses that you may find useful, so if you can choose only one block to focus on, King's Landing isn't a bad choice. If you'd like a couple examples of shadow-based burn, here's a link to a decklist of mine that did well competitively, and here's a link to the 3rd place 2010 World Championship joust deck (played by Erick Butzlaff, who is also the overall 2010 World Champion) that was Wildlings + shadows burn (again, playing shadows for the draw and added burn, with wildlings to win challenges). The "The North" agendas have been errata'd since then, so you can't play five agendas anymore, but an updated decklist would still look pretty similar.

If you prefer to focus more on dragons, then you should still play some burn. For example, Dragon Attack (Change of Seasons chapter pack) isn't bad, and you should definitely play the Forever Burnings and Flame-Kissed even in a non-burn Targ deck. The chapter pack that contains Dragon Attack also contains Maester Aemon (a great Targ card), as well as Wintertime Marauders and Game of Cyvasse, which are both staples for their houses (in case you want to build non-Targ decks in the future).

Just to add a few more cards that are in every Targ deck I build...

• Forever Burning (I think 3x is the best, but if you only have 2x and don't want to $40 for a third Core Set, then that works)
• Flame-Kissed (Again, I like 3x, but I sometimes cut this to 2x if I really can't make room and am playing other burn already such as Dragon Skull)
• Hatchling Feast (2-3x if you're running enough influence, these are brutal when combined with Threat from the North. These are kind of annoying to get ahold of though, since the chapter pack they come in contains only 1x, and the rest of the cards in that pack won't help your Targ deck much...it's kind of hard to justify spending $30 just for a playset of this one card.)
• Danaerys Chambers (at least 1x, though I often play 2x if I'm running more than 6 attachments)
• Carrion Bird (3x...these should be in almost every deck you play, as they're cheap characters with stealth and also to protect against opponent's summer/winter decks. If none of your friends are playing with seasonal effects, than it's OK to forego these. But if you ever plan to compete in tournaments, you'll want at least 2x in a deck to protect you against opponents' Wintertime Marauders, etc.)
• Ser Jorah Mormont (At least 1x in every Targ deck you build. He's probably the most efficient Targ character there is.)
• Refugee of the Plains (3x if you have space. Unless you're playing the Knights of the Hollow Hill agenda, these guys are crucial for improved setups and helping to keep your gold curve low)
• Meerenese Brothel (I like 1-2x of these, depending on whether I'm playing 2x or 3x Dragon Thief. This location is great for discarding problematic attachments, such as Frozen Solid, or other character attachments that save your opponent's characters and/or prevent your Flame-Kissed from doing it's job.

Hope this helps!

I forgot to mention that my comments are generally assuming that you're looking to build a tournament-worthy deck. If you're playing more casually with friends and looking to spend as little as possible, then you can probably fudge a bit (for example, only 2x Forever Burning, exclude the Hatchling Feasts, etc.) and still have a fun but decent deck.

One final addition: I would include at least 1x Val (Return of the Others) in every deck you make...Targ or otherwise. I know not everyone agrees, but I suspect you'll find a use for Val, especially in Targ. In fact, most of my decks include 2x of her.

Thanks!

I'm not (yet, at least) aimed for competitive tournament play, but the advices are still valuable, and at least now I know what I should be looking for.
Really helpful comments from the three of you, thank you!