There are a number of healthy, usually low cal, options on here. I tend to simply refer people to the food pyramid, google search job, and recommend following that.
Activities to recommend rely a lot on what you are used to, and what you enjoy.
If you are used to virtually nothing, just go for a few walks. If this is too boring etc. do some beginners low impact aerobic sessions, there will be videos on you tube for these. Remember low impact means at least one part of your body will be in contact with the ground at all times.
If you are used to activity, this will be too basic and it may be more suitable to do a circuit session.
Key here is being honest and realistic with yourself. If you are just a little out of practice and have a reasonable core level still great, if not and you train as if you have, it will not be maintainable, and you risk injury. This shouldn't be something you want to fix within a few weeks, you need to look at this as a long term project with one eye to now and another to next year.
Be aware the gyms will be heaving in the new year. Persevere through January and you will find the experience a lot more pleasant and less crowded. Be careful not to try competing with others in the gym based on appearance. Many do more than they should then leave, watch them by all means but don't imitate them otherwise you will want to leave too.
