Having a truly dedicated space is really ideal. Not only can you set it up exactly how you want it without any "but what happens when someone wants to watch the game tonight?" Thoughts, but I completely agree it has big psychological implications for yourself and your students.
From a "self" point of view, one of the biggest challenges of working from home is that you are at home. Almost every resource on working from home, or starting a home business encourages you to have a dedicated space. This means you can physically and mentally "go to work" but you can also "come home" at the end of the day. If your home office is actually your kitchen table, how do you have dinner without thinking about work, or work without worrying about what's for dinner? You associate certain spaces with corresponding activities, and you create a lot of internal conflict when your living room that is supposed to be a relaxing space is also your home studio where you are supposed to be focused on work.
From a student/customer point of view, it makes a big difference as well. If your lesson is happening in a professional looking dedicated space separated from the rest of the home, you approach it differently than if it's in the living room with leftover take-out and other clutter lying around. Especially as you attempt to establish yourself, build a studio of students, and encourage money out of students'/parents' pockets, presenting yourself professionally is important.
A dedicated space might not be practical for numerous reasons. You have to be able to justify the additional expense of having the space, and it doesn't make sense to rent an apartment that is an additional $300/month because it has an extra bedroom, if you're only bringing in $400 in revenue from that bedroom. If that is the case, then do whatever you can to make a shared space seem like a dedicated one. That could mean extra storage so you can quickly put away anything that shouldn't be out during a lesson, to making sure you can shut your cat in a different part of the apartment so it is not a distraction. Likewise, if you have roommates or a partner, they have to respect your work environment and not be interrupting as was previously mentioned. Other considerations are noise and whether or not you can legally have a business in the space (also mentioned) but accessibility is huge as well. You might be comfortable carrying your bass up to a second floor walk up, or taking two bus transfers from a major route, but your students might not.
I am positive there are several other factors as well, but you also have to accept that you likely will not have your dream location if you're just starting out. Do the best you can, and make sure your teaching is fantastic, and your students will overlook the lava lamp on your end table.
