You want your new weight to be a mix of a little bit of fat (slight amounts of fat is both healthy and necessary for your body to function) and a good bit of muscle (which weighs a lot more than fat). I'd suggest eating healthily with a diet focused on protein. Drink at least eight glasses of fluid a day - preferably water or tea/coffee with no sugar. Sugary drinks such as fruit juices, soft drinks and (especially!) energy drinks should be avoided. Try eating more fresh or tinned fruit for vitamins and also chicken-based recipes with carbohydrates and vegetables thrown in - a favourite of mine is chicken fillets with basmati brown rice, basil and assorted steamed vegetables. Quick and easy to make in a pan! A good book for similar recipes is Nosh For Students. Also, if you start practising cooking with these recipes now, it'll all be so much easier once you're in Halls. On top of that, make sure you both sleep well get some exercise.
For sleep, I'd recommend turning off electronics (like laptop, phone, etc.) at 9pm then getting ready for bed. If all goes well you should be in bed and ready to sleep by 9:30pm. From there, read a book or magazine until 9:45-10pm, then lights out and off to sleep <: Have an alarm set for 7am the next morning. After a few days of this, having a consistent sleep schedule of 10pm - 7am, netting you an awesome 9 hours every single night, regardless of whether it's a weekend or weekday will vastly improve your circadian rhythm's accuracy. You will feel a lot less tired during the day, feel much better waking up in the morning, feel more confident, be able to take in and retain information much faster and for longer (important for study!), feel less inclined to eat sugary/unhealthy foods and your metabolism will stabilize. The overall effect will be that it'll be much, much easier to get through day-to-day life in general and maintain a healthy eating pattern that'll help you gain the weight you need. Life feels so much better when you're not horribly sleep-deprived all the time.
For exercise, you don't necessarily need to hit the gym and follow a hardcore weight-lifting regime (unless you want to!). Simply get outside and do stuff! I personally really enjoy day hiking, which is something I picked up from my old DofE and Ten Tors expeditions. Pack a rucksack with supplies like a lunch, first aid kit and lots of water, then go out and walk off into the countryside for a few hours. I like to try and find new locations I didn't know were near where I lived each time. You could bring a phone with Pokémon Go if you're into that kind of thing or similar interactive VR apps to make things more exciting - personally, I always set up playlists of my latest favourite music and bring a pair of headphones with me. Another great option are Audible audiobooks. Walking/hiking is great exercise for almost the entire body and will allow you to build up muscle in you legs and core body, and it can be fun, too! Whilst it won't build up your arms much, hiking does improve your aerobic endurance. After a few months of occasional day hiking, you'll find that lifting weights in a gym won't tire you out anywhere near as quickly as before the hiking.
There's also the option of eating a horrifying amount of junk food, but - this goes without saying, really - don't do that. Your body would suffer horribly for it due to nutrient deficiency and an overload of generally unhelpful and even harmful chemicals. You would end up feeling very unwell almost constantly, experiencing fatigue, nausea and (quite possibly the worst side effect) develop an addiction to sugar, which is how most cases of eventual obesity start. I'm overweight myself because of this. Trust me, it's not a road you want to tread. Stick to the tips I've given above and I promise that you'll gain weight healthily in good time!
tl;dr - Eat healthily with more protein, sleep well and do some moderate physical activity where you can <: