Hi - I have done my first solo trip in Himachal as well. What I would suggest is to start with places that are easier to reach and are slightly mainstream. This will make you get some confidence on your ability to do solo trips too. Since you haven't mentioned how many days you want to travel - I am suggesting a 8-10 days of travel. That being said - I would suggest you start with the Parvati valley. It has a series of good places like - Kasol, Malana, Tosh being the more popular ones. You can spend 4-5 days total in these places. You can find multiple cheap stay options here. No need to fret too much about the rooms as you would anyway spend your time in the cafes and the mountains. From here, you can try and visit Manali (would recommend staying in Zostel, Manali for about 2 days). And if you have time then go for Bir (2 days) as it has amazing paragliding places. Transportation - To travel to Himachal, you can take a bus from Delhi. Post which, local travel between the towns can be done in local buses. They are generally a shorter journey and local buses, although crowded, but are part of the experience too. Preparation wise - I think you can definitely take with you a jacket, windcheater, thermal inners, sport shoes (So you can trek if you want to), music in phone or ipod, standard first-aid kit (as it is a solo trip), a good camera. Hope this is helpful! Good luck!
Always prefer to travel in buses. I would suggest you to go to Mcleodganj, Kasol and Manali. Do not stay at a place for more than 2 nights, as you can cover all the main places in 2-3 days. Stay in hostels, and they are cheaper and when you're travelling solo, you meet fellow solo travellers in hostels who might help you with different stuff. I would suggest do not take much luggage with you, just take the essentials, and woollens, and you can buy clothes from there also.
I would suggest you to travel to Kasol- Kheerganga-Manali-Shimla (In your return). Assuming that you are travelling from Delhi. Considering the given route, maintaining itinerary shall be easy. Leave for Kasol at night from Delhi. You will reach Kasol in morning around 8-9AM.
Day 1: You can easily get a place to stay. Relax for a bit, get freshen up. Explore nearby cafes, eat good food and chill. Buy something to restore for Kheerganga from German Bakery. Day 2: leave for kheerganga during early morning, you will get shared cabs till the point where trek starts. Spend a night there in camp. Feed on restored food. Enjoy the hot water spring. Day 3: trek down and take a local bus to manali. enjoy exploring Manikaran. and rohtang pass, if you have time. have maggie in mountains Day 3: take a bus to shimla on day 3 itself. Stay at Simply Shimla: The Kothi. You will have homely and cozy stay there. I had stayed there recently and also, wrote a review. Day 4: explore mall road, shop there. have ice cream. Cafe SOL is the best cafe of Shimla to eat at. You can also, stay back at Manali or Shimla for more relaxed trip as you have 5 days. Book your buses at red bus and where red bus is not available, travel by local bus. Things to carry: 2 pairs of jeans along with t-shirts/ tops (whatever suits you), 3-4 Yoga pants along with t-shirts. Trekking boots. Jackets, lip balm, sun-screen, extra socks. sunglasses. I guess, you will be good with this Happy Travelling!
For preparation part - take one jacket with you and good shoes if you are up for a trek.
Transportation preferably private vehicle if budget is not the issue.
Clothes- one or two pair of woolen.
4-5 days and these many places dude see for the main attractions that you will easily get to know as soon you reach there.