Shred is a great dvd to do at home and it will definitely get you to a level of fitness where you could join in a class no problem, but I wouldn't let being a complete beginner put you off starting classes or a gym straight away, there are always one or two beginners everywhere, many more at this time of year! Just make sure you have an instructor who knows you are new to it all so they can keep an eye on your technique and make sure you aren't overdoing it.
Ideally your training should include some cardio to work heart/lungs and burn fat and also some resistance training, ie weights, but this can be done purely with body weight exercises (eg push ups, planks, squats, lunges), a body pump class would also cover this if you prefer a class to the gym. Lots of people, women in particular, don't do enough resistance training but it is very important for maintaining bone health and metabolism as we age.
IMO the real key to maintaining motivation and routine is finding something you really enjoy. For me its kickboxing and I also go to the gym and run/ swim, but regard the weight training etc as ways of improving my kickboxing iyswim. So think about any sport you could picture yourself enjoying and give it a go, you may discover a passion or talent!
Running - try couch to 5k programme, on a treadmill before it gets warmer?
Swimming
Dance- zumba or ballet?
Team sports, netball?
Badminton/tennis
Martial arts/boxing
If you join a gym could you afford a few sessions with a personal trainer? This would be ideal but if not make sure you use the gym staff as much as possible for showing you machines/exercises, drafting a programme for you.
Good luck, it definitely does become addictive over time, especially if you find your "thing"!