I thought we had a sticky geared for beginners but maybe I'm thinking of something else.
Beginners and experienced people alike can use the same types of programs, what varies would be the weight and also beginners need to learn the movements before trying to max out the weight they use.
I'd recommend reading through Stumptuous, it is a great site and there are some recommended weight training programs listed on the site.
Definitely read through the site but also here is a link to the workout ideas portion of the site:
Many of us really like The New Rules of Lifting for Women
. It is a book and really covers all you need to know to get into weight lifting as well as providing you with a 6 month training program.
Another book option is Body for Life
which again provides you with a training program but it is shorter than New Rules of Lifting for Women. They also have a website http://www.bodyforlife.com
As to what equipment you would need, that depends on your resources. Dumbbells are the most basic equipment and are pretty versatile. The drawbacks are they are heavy (ie not very portable) and can get expensive and then they can start taking up a lot of room. If you can swing it, you might want to look into adjustable dumbbells but you may just want to start collecting dumbbells as you go.
For traveling/portable weight training, I'd look into resistance bands and we do have a sticky on resistance bands. Resistance Band Workout
The two programs I mentioned above done use resistance bands but if you really wanted to, you could probably modify both to include them. You could also find various routines online.
If you want really portable but also really effective, I'd also look at a TRX system. It basically uses your body weight to give you an overall workout. I have one and my husband almost exclusively uses it for exercise. It is amazing how much his body has changed in the last few months of using it. Only issue is you'd need to anchor it. They sell something so you can screw into the ceiling to anchor it as well as something to anchor it into a closed door (door must close towards you!). You can find exercises for it online, youtube has a bunch but they also sell DVDs that also come with a book showing the exercises. I have another friend who has one and she makes up her own routines based on what she finds on youtube but for a beginner, I'd say pick up a couple of their DVDs to give you an idea of the basics of a routine.
The only specific issue I'd say is be aware of your form at all times. You may not know the exact right form but you should be in control, your core should be tight and your back straight.
Also, ExRx is a good site that has many exercise demos on it and good to look through although it existed way before youtube so you can find a lot of stuff on youtube these days.
We also have a sticky on Kettlebells, which I think are a good supplement to your workout routine as it is kettlebell workouts also incorporate cardiovascular training, work your large leg muscles and are supposed to be good for your shoulders. And also definitely works your core.