I've been pushing my home computer repair biz for the last 7 months. People say that it takes 2 - 5 years to get a solid customer base. You might get 1 - 2 customers per month from your website. Postcard ads have been a break even for me, which is a good thing. Verizon screwed me with my yellow pages listing (inexplicably deleted!). Be sure and send them MULTIPLE reminders or you will be missing out on a year's worth of customers. Verizon has a sister company that puts out the yellow pages. Be sure and let them know too.
Do a combination. For my business I'd say it's about 50/50. I charge an extra $20 to pick up their computer if they don't want to drop it off. Some people want to save the money or don't want people visiting their house, while others (especially businesses) just can't stop what they're doing to get to your location. Check your local zoning laws to make sure you can run a repair business out of your home with customers showing up at your home.
I don't have insurance, and I plan on dissolving my S-Corp, because it's a waste of money ($800 a year in California + tons of formalities to follow, plus Turbo Tax, etc, etc). Incorporating is a whole can of worms and if you don't follow the legal formalities a litigant will "pierce your corporate veil" if they sue you. The purpose of either a Corp or insurance is to protect against a catastrophic lawsuit. But you can have just one good first line of defense by simply having a bullet proof contract that the customer signs. You can model your contract based on other business' contracts. They are all very similar. Essentially you are not liable for data loss, and disputes are settled in small claims court or by arbitration. A lawsuit over data loss could potentially be for a LOT of money. Once protected from a data loss lawsuit (via contract), what's the worst that could happen? You fry a motherboard? You get my point. Incorporating or liability insurance is overkill and expensive.
What if there is a problem you cant fix? I sometimes TURN DOWN jobs that appear to be too much of a wild goose chase, such as if someone wants to effectively get a new computer by getting a CPU upgrade, or if someone is troubleshooting a complex software program such as Final Cut Pro, Pro Tools, etc.