Impressions

Finally You have come to the stage where your game development has just reached...almost alpha.
Srsly? It's just the right time to paint it with the right music and sound effects. woohoo.

Um, So which way to go?

Should I browse through heaps of (questionable) categorized sound effects picking one by one?
If you have very little audio assets, lots of time and small change, yep.
Although you aren't a sound designer, picking up some skills and freebie editing programs could be worth the time.
No, there's no but coming. As a sound designer I have no problems with developers grasping the basics and perhaps have more appreciation when the goal is more professionally achieved by the sound guy.

There are about 4 large free sound effects websites which are great resource.
And, if you couldn't find what you are looking for you can always spend a few dollars, or get a package deal for yearly usage. Congratulations. You've just assigned a budget for audio. And here is where the but is coming.

Budgets are a drag. Every developer needs to start managing it and let go of the art directing work, because he knows its important. It's about prioritizing your money vs the crucial assets you need for your game. Maybe you want that cool character builder, or map editor, or hire someone to make a hip trailer.
That's tough decisions because almost everything is crucial.
My point? If you already planned a budget and it has audio in it, consider the option between hiring a guy or go to a library.

The audio guy
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There are a few things to check so you won't have a bad experience or worse, get your project slowed down and "painted" badly.

Who is he?
if youre starting out it could be some anonymous dude from the forum?
Not a problem really if he has a portfolio. Check if its reliable, like did his projects really came to be? and what reactions people had to them.
Some dudes are starting out the same as a newbie developer, so that's a good thing to work with them if you have the patience to train them and if they're willing to be cheap enough for you :p.

Back to budgets and excessive time consumption:
You were saving some for the audio guy, you're past your first game now. This is your second and you want more out of your game. Terrific. How can I check if he can deliver?
Just ask him to do you examples of your requests. That's how you know which one of them is best suited, and it doesn't have to be the most experienced. You could be surprised.
Lets say you have 100$ which is medium low budget for an average flash game.
For that amount you should get a very decent audio package if the guy knows what he's doing. And that's for sound effects only. I can't say how many sounds will you get.
Music is usually the expansive part if you want quality. It takes a good deal of time and a good deal of today's technology to get a competitive music track.
That's another thing worth mentioning, that we are in a competitive market. I see tons of fantastic ideas at the indies, but only a handful get proper funding and crew to manifest the Vision to reality. Because those that weren't aware of what's out there got trolled out by the ever cruel eye of criticism.
So getting pro music is another step up for a more competitive game obviously, but if you got your budget this far, it must be worth it.

Getting a unique soundscape for your game is an obvious upgrade, but it doesn't have to be as expansive as you think.
Especially if you already saved the budget for it.