Right now, Zekrom/Eelektrik is a pretty clear BDIF (Best Deck In Format) thanks to its consistency and raw power. The base elements don't cost too much, and give you a good bunch of cards to base future lists off of, so it makes a great first deck to build upon. One of the great parts about this deck is that it will also be largely unaffected by the rotation, since most of the cards are BW-on.

Here's a sample decklist:
Pokemon: 15
($173.00)
2 Smeargle $4
2 Zekrom $2
2 Mewtwo EX $120
1 Raikou EX $18
1 Tornadus EX $25
4 Tynamo $1
3 Eelektrik $3
Trainers/Supporters/Stadiums: 33
($7.50/$60.75 = $68.25)
4 PONT $4
4 Juniper $2
3 N $1.50
2 Dual Ball $1
2 Level Ball $1
1 Ultra Ball $1
1 Random Receiver $2
2 Plus Power $0.50
2 Switch $0.50
4 Junk Arm $16
4 Pokemon Catcher $36
1 Super Rod $0.25
1 Eviolite $1.50
2 Skyarrow Bridge $1
Energy: 12
($4.00)
4 Double Colorless Energy (DCE) $2
8 Lightning $2
Total Cost: $245.25
Cost of Staples: ~$220.00
Alright, so I know what you're thinking... How the hell is a $250 deck considered budget? Well... how this thread is formatted is to provide you with a good list of the deck and then offer you budget replacements if you feel that you don't want to spend the extra money for the optimal list. So this deck should be displayed no different, it's just that an optimal list costs a lot more than the other decks. I'd add that there are many different flavours you can add to ZekEels to personalize it to become your very own, so the list above is by no means a set standard "best" list.
The cost of the staples of this deck is also somewhat inflated. This is because I'm including Mewtwo EX and Tornadus EX (not Raikou EX) in the staples category. Mewtwo EX is obvious, but Tornadus EX isn't as much, so I'll quickly elaborate. I think having 1 Tornadus EX can be considered a staple since it's so useful in so many decks. The idea of listing the staples cost is to show how much of the deck's cost is going to go towards cards that can be used in multiple decks. i.e. How much of your investment will be useful outside of this one deck? If you're going to play on a budget, it's good to be smart with your money and not spend too much erroneously on cards you'll never use again. So the "Cost of Staples" listing is used to inform the reader that the rest of the cost is less splashable in other decks.
To provide a quick blurb, this deck's strategy is to hit hard, fast and consistent. Pretty difficult to see what can go wrong if you pull that all off, and this deck has got the goods. The list above is equipped with 3 different EX cards (4 total) to help you out when facing many aspects of the metagame. Thanks to this toolbox, the deck can deal with practically any deck you throw at it. Just use the right attacker for the right situation.

Now, considering this is a "Budget Decks" thread, how can you build this tier 1 powerhouse for cheap? Well, here's another sample list to get you started:
Pokemon: 15
($20.00)
1 Smeargle $2
3 Zekrom $3
1 Zekrom EX $6 - (optional, could run another Zekrom BW, but Zek EX really helps this build out)
1 Thundurus $1
2 Tornadus $4 - You could also use Zapdos @ $0.50/card
4 Tynamo $1
3 Eelektrik $3
Trainers/Supporters/Stadiums: 32
($7.50/$53.25 = $60.50)
4 PONT $4
4 Juniper $2
3 N $1.50
3 Dual Ball $1.50
2 Level Ball $1
1 Ultra Ball $1
2 Random Receiver $4
3 Plus Power $0.75
2 Switch $0.50
4 Junk Arm $16
3 Pokemon Catcher $27
1 Eviolite $1.50
Energy: 13
($4.00)
4 DCE $2
9 Lightning $2
Total Cost: $85.00
Cost of Staples: ~$70.00
Here we have a fairly similar build. The core of the deck remains largely untouched, but there are some obvious and big differences.
First off, we've cut our old EX's. Our wallet was too tight to justify spending so much on only 4 cards. However in their place we have some alternate attackers. The deck is now running an extra Zekrom, Zekrom EX, Thundurus and 2 copies of Tornadus EPO. The deck is definitely looking to add a couple mewtwo EX if it could, but Zekrom EX has been added to provide a behemoth that can stand up to Mewtwo EX and come out in an approximately equal exchange. Without this card, any deck running a couple Mewtwos will beat you down by loading energies onto Mewtwo. Zekrom EX is only 2 Pluspowers away from 1HKO'ing Mewtwo.
Tornadus serves a slightly different role than its EX counterpart, but they're both included with fighting decks in mind. The biggest difference is in how aggressive Tornadus EX is. Getting a tornadus EX out first turn can donk with a DCE and stadium in play, and even if you whiff, still threatens a turn 2 100 damage. Tornadus EPO can do neither of these things, but at least can threaten a turn 2 80 damage. However we now have included an attacker that can do this job much better. Thundurus.
Charge gets you a consistent turn 2 80 damage which can probably take a prize with a pokemon catcher. If you're on a budget though, you could run a pokemon circulator or reversal. Unfortunately, this is all I can recommend on a budget beyond cutting the EX's. But at least know that your buck should go a fair ways in allowing you to build more decks in the future.
The last big change which probably doesnt SEEM too drastic is dropping the skyarrow bridge and one Smeargle. Without Tornadus EX, Skyarrow Bridge becomes far less useful. You just have to be pro-active about dynamotoring an energy onto smeargle before you have to bring it out, to help make sure you can use it appropriately.
As I said, this deck doesn't really have many switchouts for a budget option, but it's not so expensive that you can't build a pretty competitive build for not too much. The minimum cost of $59 comes from dropping three catchers and adding three reversals or circulators.
Minimum cost: $59.00, Maximum cost: $245.00