I want to join the army reserve, but I don’t want to travel far for training and stay away from my family for long

The beauty of the Army Reserves is that you can have the best of both worlds, be part of the Army but not have to move away. You should google where your local Army Reserves unit is and can give them a call. They will invite you to a training evening to see whether it's for you. Army Reserve initial training is 2 weeks - where you wouldn't really see your family however normal once a week or once a month weekend training would be relatively close to your home. You could end up doing courses that would mean you'd be away from home but it's very rare that they are longer than 2 weeks as they are designed for civilians who have a full time other job and Reserve training needs to take place during their holiday period (although many employers now grant Reservists an extra 2 week holiday a year under the Military Covenant). There might be a chance that you could be mobilised but that would be very very remote and rare and 99.9% of Reservists who mobilise have done so because they have volunteered for it!