What are the various mountains which are great for beginners? mountains which requires some form of technical skills instead of simply trekking up

Your best bet is to pick up a local Scrambling guide. Scrambling is hiking and easy climbing in exposed (high up, with lot's of air bellow) places. Generally it is a summer activity, and is a good way to get used to mountains, and exposure. Some routes can be done in winter. When you are looking at getting into more technical mountaineering there are really 4 main skills you need to build. The first is navigation. You should learn to navigate a mountain properly, to figure out where the line of least resistance is and how to get there. It is something that is really built up over time by doing many routes. Each new route will hopefully make you more confident, and experienced in decision making. The second skill is dealing with exposure. I know this is my weakness. Exposure is the sense of being high, and unsafe. It slows you down on technical terrain and causes you to waste energy by tensing up and messes with your headspace making the ascent more challenging. Like route finding this is just a matter of experience. Equally important is technical skills. This can include things like crevasse rescue, rope management, knowledge of when to use ropes and when not to. Ice axe arrests, and crampon technique. It's a pretty broad category, and is one that is best done through some formal means, i.e. courses or something of that nature. And lastly fitness. This is important as endurance and strength will help you in the event of a emergency, and increase your chances of success, as well as prevent injury.  Mt Rundle in the Albertan Rockies is very accessible, and great in winter if your aware of avalanche conditions and carry a ice axe and crampons. In the summer it's very straightforward. If you want something for summer that is a better challenge try Cascade Mountain. Near Vancouver, Canada, the West Lion is a popular route, or you can try fro camel mountain near Grouse. Easy access, but not safe in winter. In the UK I recommend Fiacaill Ridge in the Cairngorms. Great all year around. Requires crampons and axe in winter. Whiteouts are pretty common, so make sure you've got good navigation skills, compass and a map. In Europe the Alps are pretty big on alpinism. There are some scrambles, though you'll also find Via Ferrata in the southern Alps. It will give you some technical abilities without the risk, but it doesn't give you as much of a head for heights as you should desire as your constantly protected in the event of a fall, and the route finding is done for you. In the states I've heard very good things about Mt. Rainier, but it probably requires more experience, or alternatively a guide, or someone who has mountaineering experience. For pretty much everywhere with topography should have some scrambling options. Always a good place to start. Edit: A bit controversial, but generally I wouldn't say that indoor rock climbing has much use for mountaineering except teach you the basics of rope work. While it can be a fun introduction, it teaches you many bad habits. The main challenge in beginning mountaineering is getting used to, and comfortable at heights. Remember much of what you'll be ascending would barely be a challenge at ground level. You can easily walk across a 1 foot wide beam in your local park even when it's very windy, or climb on top of some clumped boulders. But if that beam was 1000 feet in the air, or you had to climb up for extended periods of time, you may desire crossing it on your stomach, and wouldn't say no to a rope if it was offered. Indoor rock climbing builds muscle, and skills to pull technical moves in a very safe, secure environment. Routes are colour coded or marked, so you aren't required to think about the route until you start climbing above 5b/ 5.9 . On rock you have to be much more aware, and thinking about your route, your body, or just trying to unlock the puzzle of how to move to best get up this route. These skills are necessary for climbing indoors at grades generally that require too much strength for beginners. Hiking and Scrambling anywhere is your best introduction. Build your endurance, your stamina and resolve. Get used to heights, navigation and pushing yourself when you don't think you can go any farther.

Mt Shasta is a great starter mountain. The Avalanche Gulch route is relatively straightforward, but requires an ice axe and crampons. If you know the basics of mountaineering, like the self arrest, you can go without a guide. Or, try a local guide service to show you the ropes.