New Game Plus:
After beating the game, you can start a New Game + from the main menu, carrying over the stats of a character from any savegame after the main mission ending. You carry over all levels, skills, credits, research data, and items (except quest/story items), but do not carry over Codex entries or Cryo Pod perks. The latter is important particularly if you used a perk to expand your inventory- you may now have more items than you can technically carry. The game won't destroy them, but you won't be able to pick up anything new until you get back under the limit. For this reason, it's a good idea to visit a store and sell or breakdown all your extraneous items *before* initiating a New Game+.
Your choices in the first game do not carry over into the second- you can switch up your gender, appearance, and background at will. Skills will stay commited, but you can use the Respec station aboard the Tempest as normal.
Note also that the universe responds appropriately to your current level- enemies will be of a similar level, and loot will match as well (ie you won't be finding any level 1 weapons or armor).