L.H.
My son taught me lots about ukes. He fell in love with the ukulele after hearing the songs, "I'm Youre's" and "Hey Soul Sister" by Train. Train uses a tenor ukulele. The best link to go to is a website by Aldrine Guerrero
called Ukulele Underground. http://www.ukuleleunderground.com It is a must for you to look at that website, because Adrine gives free lessons and lots of info. about the ukulele in hopes to revive it. His uke play along videos are alsome and show you that the uke is not a toy. His uke minutes answer all sorts of questions.
Ok now on to answering your question: You want to get a good uke, so you're not buying another in 4-6 months. Cheap ones like those $20 ones, just aren't going to do it. They don't have the right sound/timbre. The more expensive ones have more warmth. You can even try Ebay to get a good quality used one. There are 2 types of tuning knobs...One is the friction tuners and the other is the geared. You want the geared tuners, because they hold the pitch better and keep it in tune longer. Nothing sounds worse than a uke that is out of tune. (You can also find a free online uke tuner website, so you don't have to buy a tuner.) There are 3 sizes: Soprano/Standard, Tenor, and Bass. Do not get the bass, because it sound too much like a guitar and has the same tuning as a guitar. My son's first uke did come from Amazon and it was a Makala soprano. (Don't get the Mahalo, it's not as good as the Makala.) Makala is made by Kala and is their economy uke. I think it was $35-39 when I purchased it. Now, it's $41.50. Beautifule sound. My son's second uke was from SamAsh (A music store that also sells stuff online.) and is a Lanikai LU-21TE, which is an acoustic/electric uke for $129.00, but now it sells for $170.00...that thing is amazing! The Lanikai can sound like a typical uke or like an electric guitar. You just can't beat the sound quality and it came with Aquilla strings, which have a guarentee and are one of the best strings you can buy. I will admit to going cheap on the amp. I got it off Ebay for $20. It's a little Kustom 10 amp. For Christmas I got him a VOX wahwah pedal at Guitar Center for $79.
My son plays "You Look Wonderful Tonight," "Fur Else," "Pokemon Theme Song," "Obla-Di," and a bunch of other stuff on it. He actually prefers it over the guitar, because ukes are a lot lighter and will play it in the school rock band. (So far, his school band is the only one in the state with a ukulele player.) The problem is that there isn't much support for the uke; however, you can find lots of free lessons and chord charts for it on the internet. Hope this helps.