Honestly, I wouldn't bother rushing it. At the end of the day, Mew is nothing but a dex entry. Even if you were to get the best moveset on your Mew and max it out, it would still have limited uses. I highly doubt that your Mew will be un-claimable come the release of Celebi, take your time for your awesome AR shots.
GamePress
Should I rush to claim my Mew?
A few weeks ago, I finally managed to land an excellent curveball throw, but I have yet to claim the rewards because:
1. At level 38, XP no longer benefits me.
2. I have no pressing need for 20 Ultra Balls (until there is a major stardust event) or Mew.
3. Item and mon storage almost full. Saving up gym coins (hard to get in my highly competitive area) for upgrade.
4. Thinking where I could take great AR shots of Mew and saving real money to upgrade my four-year-old iPad.
With Celebi about to be released, should I rush to claim my Mew? Guess I could spend those Ultra Balls on some cheerleaders for bonus stardust...