Depending on where you live, rent payments for a 'brick and mortar' business may be higher than the benefits, so I'd first consider the reasons for wanting a 'brick and mortar' business. What advantages come with a shop? Here are the main ones:

1) It allows easier discovery by people that happen to walk by (i.e. a form of advertising)

2) It provides a reputable looking place where people can come to transact (i.e. dropping off their phone there instead of dropping it off at your house)

3) It provides space to do your work.

All of these things are important for certain kinds of businesses, but I'd say it's not as important for phone repair. At least not while you're starting out and testing the waters. So as Chalmers suggested, you should try starting out by just doing repairs with whatever resources you currently have available. There are several ways you can do this while still having the advantages of a 'brick and mortar' listed above. For instance, in the same order as above:

1) Post signs about your services around your neighborhood (phone poles, etc.). You might be able to get permission from certain local shop owners to post signs in their shop too (for instance coffee shops, bookstores, libraries, colleges, etc.).

2) Try to find a local shop owner that would be willing to act as a drop off point for your customers. Try to find someone that you're pretty sure you could maintain a long lasting relationship with, you don't want to have to change your address frequently. Shops that would be most interested would be those that would either A) potentially get business from the same people that are dropping off phones. For instance a coffee shop, or a pizza place (after dropping off a phone someone might also buy a coffee or slice of pizza), or B) be providing a useful additional service to their existing customers, thereby enhancing their relationship with them. For instance, maybe there's a computer repair shop that doesn't know how to repair phones. By having you repair phones through their shop they'd be increasing their range of services.

3) You shouldn't need all that much space to repair phones, at least not when you start off. Buy a cheap $30 desk online and set it up in your house to use for repairs.

With those solutions, you've now got 90% of the advantages of a brick and mortar without having to pay the rent. So you can spend that money on online advertising, etc. instead. You can do geographically targeted advertisements on Google adwords, so you could start with that. Make sure to set up analytics for your website too, so you can measure how well your advertisements and landing page work. After you've started to get business and a reputation then you could consider setting up a brick and mortar shop of you think it's worth it.

If you'd like more in depth and specific advice related to your specific situation, or related to your online presence, let me know, I'd be happy to help out.

best of luck,

Lee