invest in good base layers, they are worth it. take a spare if you're going over night so you can sleep in something dry. every big box brand has base layers most of them are fine. under armor probably isn't the most economic but they're level 1, 2, 3, 4 system is very easy to understand. you probably want something like 2, 3, 4 one of each both tops and pants. get at least 2 pair of good wool socks. i like darn tough but smartwool is fine too, wear a liner sock to absorbs sweat like the Fox River Outdoor Wick Dry Alturas. this should be form fitting, not constricting but a tad tight. then wear the wool sock over it. take 2-3 pairs of liners and 2 pair of insulating socks. take some kind of boot, 20, 30 degrees doesn't really matter you will be fine. make sure you have a hat and decent gloves. my favorite value brand is
32degrees.com, lot of bang for your buck with their stuff, im wearing one of their shirts right now, you can make a solid entire wardrobe for around a 100
learn layering. you need to be able to add and subtract based on activity level. A good insulation layer for both pants and top, then an out shell. you can use most any non-cotton pants as your shell.
consume calories, yes it really makes a big difference feeling cold
tent + sleep pad + sleeping bag is a whole different conversation. try a couple 1 nighters, you wont die at those temps unless you get wet.
take rain gear. getting wet sucks and can be dangerous.
what else, take some chemical warmers. make sure someone knows where you are and when you'll be back. avoid getting wet. avoid sweating. have an emergency plan including carrying emergency blankets at at least 2 lighters and tinder. like anything you've got to get out and do it to really learn. no cotton, cotton kills.