Hello, Halehana,
Welcome to the Scotland forum! You have to start somewhere, so good on you for taking the plunge.
First thing you need to do is arm yourself with a couple of good guidebooks. The Steves' guide is good, and the latest (2018) edition includes a lot of the west and north coasts which weren't included in the initial offering. The Lonely Planet guide is also excellent, as it is more detailed, and covers many areas not covered by the Steves guide. As you'll be carrying your luggage, and won't have access to a car, best to make notes or photocopy the appropriate pages, so that you're not carrying books around with you. I am not going to suggest ripping out the pages as you go, as that is sacrilegious to me.
As a solo traveler, you'll be paying more for lodging in some places than you would if you were half of a couple. Most lodging doesn't charge 50% of the usual tariff for a single traveler; however, you'll still get some sort of discount at most B&Bs and guest houses. The exception would be hostels. Many hostels have modern facilities, including private rooms. But if you want to have exclusive use of a private room in a hostel, you may have to pay full price for the room. It all depends on the kindness of the warden.
You'll find that many B&B and guest house owners (not all) will be willing to meet you at the nearest train station/ferry terminal/bus stop. Getting to activities/sights could present more of a problem, but none of it is insurmountable. Both the guides I've recommended provide the nearest bus or train routes to various sights. As you go farther north, you'll find that public transportation is less frequent, so you may have to rely on taxi service. As you're doing your research on the internet, look for the names and telephone numbers of taxi companies in the areas you're visiting.
I'm assuming that this will be your first time in Scotland. You are in for a treat! The scenery is amazing, and the people are super friendly.
As you have three weeks, you have plenty of time to explore. However, you do need to choose specific areas that you'd like to visit, in order to map out your travels. It is a little more difficult to get to more remote locations without a car, but don't let anyone tell you that it can't be done!
Have a look through the other topics on this forum, and check out recommendations. Also, check Trip Advisor for reviews of potential lodging and places of interest.
Keep asking questions. There are a lot of people on this forum who dearly love Scotland, and will be happy to share their information with you.
Best wishes for your travels!
Mike (Auchterless)
p.s.: Don't spend too much time in the cities. There's way too much beauty in the countryside. If you have the time, I'd highly recommend a visit to the Outer Hebrides. From Ullapool, you can catch a CalMac ferry to Stornoway on Lewis; take the bus to the gorgeous beaches of South Harris; take a ferry to North Uist; then a bus down to South Uist and Eriskay; ferry to Barra; then a ferry to Oban. That will give you mountains, coastlines, islands, bird and other wildlife watching, prehistoric sites, and a trip that you'll never forget.
p.p.s.: Also check out the Walkhighlands website. It gives you information of hundreds of hikes (from easy to difficult) in all parts of Scotland. Not just the Highlands and Islands (mostly), but also city and town walks. The website also contains accommodation information. Also, if you'd like to get away from it all for a couple of days, the islands of Eigg and Rum are ideal. Both have plenty of hiking and walking activities, and are easily reached by ferry from Mallaig. Knoydart is another great place for exploring; accessible by boat from Mallaig, or a 16 mile hike in from Kinlochhourn.