I acquired my first monetized app from the original developer in October last year.
There are a ton of app and website brokerages out there, with a wide range of quality available - be prepared to kiss a lot of frogs before you find your Prince Charming!
I originally purchased my app business through Empire Flippers (empireflippers.com), and couldn't have been happier with their process and quality, but they've been gradually upping their minimum asking price for listings - I think they currently stand at ~$25k right now. Flippa.com is probably the biggest and best-known brokerage out there - I've used them several times from the sellers' side. They have tons of apps for sale at ~$5k (and lower), but tread carefully and do your due diligence: there are tons of scam and copycat apps out there by sellers who intend to take your money and leave you with a lemon. QuietLight and FE International are also fairly well-known website/app brokerages, although I can't comment as to the quality of their listings, not having personal experience with them.
You can also approach it the other way, by searching for the kind of apps you want to acquire, and contacting the developers directly to ask them whether they'd consider selling.
Hope that helps, and congrats in advance, the journey you're about to embark on is a really exciting, educational (and humbling) experience! =) I love talking about this stuff, and am happy to answer more questions, so feel free to set up a call, if you're interested. ~Jason