With seedlings you can drop that down to about a foot, closer for sure if you have a fan of any type to blow over your plants and over the bulb so less heat is transmitted down.
 
When your plants are stronger, again with a fan blowing on the tops and on the light, you can keep your light around 4 to 6 inches away. Now when the plants are really growing in flower that is a risk because they can grow into your light in a hurry so you do have to make adjustments at times but the basic idea is if you have a fan blowing on your light and plant tops you can keep a 250-watt light very close.
 
You can use an HPS from seedling to harvest. A MH for vegging is better but if I had to go from start to finish with wither a MH or an HPS I would pick the HPS every time. Of course there is the option to purchase a MH conversion bulb that will run with your HPS ballast.
 
You did not mention how much height you have to use but if you have a lot of height and were considering growing 4 or 5 foot tall plants …. don’t waste your time. When I used 250-watt lights I had both MH and HPS and I would of course veg with the MH and then flower with the HPS. Well it took me like two grows to learn that the last two weeks or more I put into vegging was a total waste of time and effort and an additional expense.
 
I would veg to about 18 to 20 inches, sometimes topping once, and then flower. I would end up with plants that were 4 to 5 feet tall, sometimes taller, and roughly the top 15 to 18 inches or so produced like a champ. Then about the next 15 or 20 inches down produced pretty well but the buds were smallish, smaller as they went down the plant, and they were fluffier. Then there would be a thin layer of popcorn buds followed by a layer of no buds and then a layer of nothing .. and I do mean nothing … the bottom of the plant where the nodes were the tightest stacked early in vegging, ...... well all the branches died off from lack of light.
 
That is when I first learned about the common over expectations about what lower wattage lighting can do and also about how easy it is to outgrow your lighting capabilities vegging and only lengthen the overall period of time from popping beans to tasting that first cured hit.