The Lenders want 2 years of employment history, particularly if you changed your job title.
There is no upper end to what you should save:
Set a goal for yourself; if you want a $250,000 house, saving 20% would mean $50,000 plus, $12,000 for Closing costs and 3 months gross income in a Savings Account.
It might be a good opportunity to adapt your life-style to a goal-oriented style: Give up the nights out, the movies, the pizzas, the new outfits, etc.
What's more important to you, the House or pizza?
Good luck and may God bless