there's the stage where you found a bunch of nekomata (were-cat chick). The geo gives them 10% level up every turn. Get some better equipments and capture the one that's around 2 times higher in levels than your best character. Rinse and repeat the process until you get level 9999
WARNING: Doing this will ruin any enjoyment you have to the main-plot of the story as it will make the game too easy. I recommend play through the first time without doing this, but that is up to you.
Level has absolutely nothing to do with capturing monsters, stats do, specifically ATK, DEF and HP, though there's also an SP explosion. Like the above poster, I don't recommend abusing huge capture chains where you capture successively stronger monsters to get to level 9999, but as a way to get a character with a high enough level to steal a particular item or to start off new characters with a bunch of stored levels, it's fair game.
Look at your main characters stats. If you've got a few characters with about equal stats to the monster you want to capture, or you can use Braveheart or Domination to bring them up that high then have them retreat to the Base Panel, then throw the monster in. You can also soften the monster up beforehand, for example by having Thieves or Kunoichis using sleep and poison, or magicians and monsters using ATK lowering debuffs. If you can catch a monster under these conditions, you've pretty much earned it, but don't go equipping it with matched rarity R39s to catch something twice as strong and rinse and repeat.
Yeah, I'd wait at least until you play through the main storyline. Once you get the Nekos, everything in the game becomes easy (at least until you get to the ultimate Baal Bosses). However, once you've completed the main storyline, getting 9999 Nekos makes things soooo much easier. Trying to work your way up to the ultimate items takes FOREVER if you don't use them (maybe five/ten times as long).
For reference, the stage is 4-3. As a general rule, you should be able to capture a Neko of twice the level of your current highest level character, though at lower levels (until you get a Neko of level ~500), you will probably want to go lower than that. You'll sometimes lose earlier on because your power character won't be able to "one-shot" them during the capturing process. Also, developing a strategy for capturing them takes some practice, so make sure you save every time before you enter the level to try and capture. Also make sure your strongest character is IN the base panel when you go to throw the monster in, otherwise you will lose for sure.