However you run Padawan selection is up to you, if you want to combine the various options and statements you could go like this:
Age 8: Younglings are first open to being taken as Padawan, many are taken as soon as they become available, or within a year or so.
Age 13: By this point, it's somewhat notable that a youngling hasn't been taken as a Padawan. If is is believed that no master will train them, they may be sent to a Service Corps, while if there is a master who wishes to take him but he already has a Padawan (or there is a shortage of available masters, ect.) he may stay officially "youngling" for a few more years, but unofficially accompany Jedi on expeditions outside the temple and beyond, possibly to prove their worth to a Master.
Age 18: The absolute upper limit, and only reachable by multiple extensions to deadlines. If a "youngling" (which by this age they hardly are) hasn't been selected, they are off to a Service Corps.
I actually like the Service Corps ideas, it fits very well with the post-Ruusan Jedi Order. The very strict, very inflexible order with the "We don't care that you've got more raw force potential than we've ever seen and you've got a Jedi Master offering to train you, you're not allowed in because you're over the minimum age" attitude.
The way I see it, given how incredibly rigid and picky the Order was at the time, especially by the time of the Battle of Naboo, many masters would be almost looking for reasons to turn down apprentices. Bureaucracy, deadlines, pride of selection and quiet shame of rejection. It sounds a lot like the hubris that tainted the Jedi Order towards the end (I'm certainly no Jedi basher, but the order had some serious internal problems, besides just Skywalker towards the end).
Too angry and feisty, too disrespectful, too prone to brawling. They are passing judgment on kids (anywhere from 8 to 18, sources vary) that seriously affects the rest of their lives. I'd imagine that a lot of Palpatine's Dark Side Adepts, Inquisitors, Emperor's Hands, and other lesser force users enthralled to him were recruited from disappointed and dejected former Younglings who had a grudge against the Order for not training them. Now, under the Emperor's New Order, their talents will finally be recognized and they'll recieve the training they deserve (or so they see it).
As a GM, I see it as a way for players to have force-sensitive characters who are citizens of the Republic who are not Jedi (their talent was discovered, they were trained, and passed over. Presumably many leave the Corps for normal civilian life. Also, after Order 66 and into the Rebellion and early New Republic Eras, it helps give a plot device of a NPC who knows about Jedi without having yet another lost Master in hiding: they were younglings who were shipped off to a service corps, quit as soon as they could/reached adulthood, and made their own way in the galaxy, so they know the basics of Jedi teachings, they are force-sensitive with basic force skills.