Help beating my brother

So a few things.  First off, the reason it looks like you're losing to your brother is because your mana curve is too high and the higher costed items in your deck really just don't deliver the sort of punch you need a 5-7 drop to deliver.  For instance, look at the difference between Armada Wurm and Voice of the Provinces.  Both come into play and create a token, but one is a 3/3 flyer that makes a 1/1, while the other is a 5/5 trample that makes a second 5/5 trample.  By the time you're getting to where you would play your larger stuff, your brother already has more value on the board (as it looks like his decks have some better value creatures).

That being said, you would benefit from pretty much ANYTHING from the RTR block as Selesnya is a big player.  Whether it be a playset of Loxodon Smiters (roughly $10), Centaur Healers (even less), Armada Wurm, Advent of the Wurm, or even just picking up a few Selesnya Charms they will go a long way for you.  Additionally, look for Thragtusk to drop even more in value in the next few weeks once it rotates.

As for attending an FNM, my suggestion would be to go to your LGS and just scout things out.  You don't have to play the first time you go, as you would benefit just getting to know some of the people, scope out what people are playing, what format it is, the cost to enter, how competitive it is, etc.  The reason I suggest this sort of peaceful fact-finding mission before just leaping in is because some FNMs are laid back and welcoming to even the most inexperienced players; but others are REALLY competitive, not all that different from Grand Prix trials - as you can imagine, you're likely to enjoy one but not so much the other.  In either event, I don't know that you're really well suited to perform well at one until you really invest a bit more on some newer cards, but you could easily still have fun.

When you say build a deck for $50 and hold up at an FNM, do you mean win?  I would say no.  There are budget decks out there,  an RDW is probably still going to be pretty cheap, but if you cap yourself so low I'd say your chances aren't good. 

Check out the article below.  The red decks you see there will be pretty "budget", but they're not the greatest.
http://southfloridamagic.com/archives/burn-baby-burn

typically when people say "build a deck for $X" it means the total value of the deck in question.  Only you know what you have in your inventory.

Sadly in order to really WIN games at FNMs you will have to drop cash.  Now, that being said, there are decks that you can have fun with and win here or there at FNMs for relatively cheap.  You're even going to benefit here significantly with rotation and the rise of mono-colored decks.  Half of the cost of a competitive deck has been in the manabase (shocks can add up if you hadn't noticed), but a mono-colored deck will let you get away with just basics for the most part. 

Start tinkering around with the cards sticking in one color and see what you can come up with.  Search the database here for cards only printed in RTR, GTC, DGM, M14, and Theros... odds are you'll be able to come up with something decent for not too much.  Mono-red aggro is one option; mono-green aggro is likely a bit weaker, but also somewhat viable; mono-white aggro (aka white weenie) is likely out of your price range given the inclusion of Archangel of Thune in most peoples' lists - although Path of Bravery apparently has potential if used correctly; mono-black control will almost certainly be an option; as will mono-blue mid-range/control - likely focusing on Thassa, God of the Sea and Master of Waves with counters, lesser used blue enchantment removal like Claustrophobia and Agoraphobia, and Aetherling - but it might be out of your price range too.

buying singles is always more efficient, but there's something to be said about cracking a pack, its like scratching a winning lottery ticket when you open something good.  Also, opening cards in packs can present interesting trading opportunities.