the budapest is okay. go for it!
it's not unsound and you can still play it against people who know what they are doing, though then white has a slightly bigger theoretical edge than usual which shouldn't actually matter that much.
when over 50% of your opponents don't actually know what they are doing (like i feel that's the case at your level), that's a nice bonus.
my main issue with having the budapest as a main staple of your repertoire is 2 Nf3.
I just started playing chess this year but I've been playing every day, and up until recently I would only play as black against 1. e4 because I was trying to learn the Sicilian.
Recently I decided I better learn an opening against 1. d4 so I could play against it as well, and without knowing anything about it, I picked the Budapest Gambit (the normal knight to g4 version not the Fajarowics variation). I figured I needed to learn an opening for d4 and I just needed to pick one and it might as well be the Budapest.
So I got the Chessbase DVD on it and started reading about it. After this cursory research I had mixed feelings about my decision to learn the opening. On the one hand a lot of what I read on forums said the Budapest was a bad opening. On the other hand, in the Chessbase DVD, the instructor IM Andrew Martin sounds very enthusiastic about the Budapest, you can hear it in his voice. I have several other Andrew Martin DVDs and in none of them does he sound that enthusiastic and amused when he's talking about an opening. I also know IM Andrew Martin is friends with GM Nigel Davies, both being from the UK, and Davies plays the Budapest sometimes in high level games, so if players of the caliber of Martin and Davies think the Budapest is good, then there must be something to that.
Most of the first 20 or so games I played with the Budapest I lost, but now that I'm becomming familiar with it I seem to be having more success with it, and I seem to actually have more success with the Budapest than the Sicilian.
What makes the Sicilian a worse opening I think are all white's ready made attack plans. If you'll remember I talked about this in my last post here. The Sicilian has been analyzed and studied so much that white doesn't have to be creative in order to beat it, white just selects a ready made plan such as the Grand Prix attack, Alapin, Closed Sicilian, etc. I think it is very telling that when I went into Barnes & Noble last week looking for chess books, the only books I could find on the Sicilian were ways to beat it such as "How to Smash the Sicilian" etc. There were no books about how to actually play the Sicilian as black. I find when I play the Sicilian I usually have to deal with a white attack from the start. Again, I've only been playing chess for about 6 months now, so all these people I play against have been practicing with their chosen "anti-Sicilian" for years and I'm having to go up against that.
With the Budapest it seems like black has the initiative more. White actually responds to what I'm doing instead of the other way around, and a lot of people don't seem to know what to do against the Budapest. It's less common than the Sicilian and there aren't these ready made attack plans against it that white can choose from at their liesure. The only ready made attack plan in the Budapest I've read about is for black with the rook lift. I have more fun playing the Budapest and I seem to be having more success with it than the Sicilian despite studying it only a fraction of the time.