When you are vacating your primary residence and converting it to a rental property or as a 2nd home, there can be some additional requirements when it comes to qualifying. There is no standard guideline which says you must have a certain amount of equity in the home you are vacating... but if you want to use rental income from the home you are vacating in order to help you qualify, then there can be.
If the new mortgage you are getting is FHA financing, if you can qualify for both your new and existing mortgage payments without the use of rental income, then there are no additional restrictions. However if you need to use rental income from the home you are vacating then you'll either need to prove you have 25% equity OR be relocating to a new area for employment (such as you are being). In that situation, then 85% of the amount you are renting it for can be used to offset it's housing payment with the end result being you can qualify for more. You need a rental contract spanning at least the first year of the mortgage and a copy of the 1st months cancelled rent check and/or security deposit. There are no "reserve" requirements for FHA financing (meaning money leftover in the bank after closing, although I do not advise being flat broke immediately after you buy a home), and the down payment can be as little as 3.5%.
With conforming financing (the most popular type of conventional financing), if you can qualify for the new and existing mortgage payments without rental income from the home you are vacating, then no issue with the amount of equity your old home has. If you do need to use rental income to help qualify, then there is a 30% equity requirement in the home - relocating for employment is not sufficient in itself. Conforming loans have reserve requirements, it can be as little as 2 months of the new monthly payment on the home, but it can also be up to 6 months months reserves for the your retained and new mortgage (depending on how much you are putting down, as well as if your loan is being approved through Fannie Mae's or Freddie Mac's automated underwriting system).
Please let me know if you have further questions.