You should think about sectioning off a portion for you recording space and insulating it from the rest of the world as much as possible.
Think long term. It's cool to just move your gear down to the basement and start making music, but consider the time and effort it takes to even play music much less record it and record it well. I have a wife and kids too and understand how valuable time is. It is hard to get time to yourself. I found that by the time I got the mics, cables, instruments out of the closet and set everything up, it was time to go to dinner, pick the kids up from school, take out the trash, got to work, wash the car, watch the kids, buy groceries, entertain neighbors in laws and whoever else stopped by, mow the grass, feed the dog, change diapers, fix the sink, clean the garage, take the car to the shop, make lunch, do the laundry, go to church, help with home work, change the light bulb, bebug the PC, rake leaves, pay the bills, return the overdue DVDs,.....
So, if you spend time on the front end doing the research and building, you can create a space for yourself where you can leave everything set up and ready to use, giving you more time later to play and record, it sounds good and helps you get better and better at both playing and production --- because all the other stuff can't wait -- I know, you've got a family to take care of.
1st the sectioning: Good for two main reasons, one: if the stairs to your basement empty directly out into the space you will have problems with wife & kids walking into a session. Two: sectioning off a portion of the basement for you recording area will also help with reducing natural reverb and reflections. You could do this by hanging heavy drapes, carpet, or fabric or if your handy- - build a dividing wall.
Insulating: You will need to insulate your recording space to reduce outside noise from coming in. If your basement has a suspended ceiling with fiberglass tiles, you already have some insulation in place - add some fiberglass batting between the ceiling and upstairs floor joists. If your basement has no ceiling and just exposed floor joists - over the are you section off, install fiberglass batting between the joists and hang Gypsum board preferably or foam panels (the smooth surface blue or pink - not the compressed white beads)
You will need to insulate your space from any noise made by appliances and mechanical equipment
Room treatments on the cheap: Once you have reduced outside noise as much as possible, you will need to treat the space for recording. As others have mentioned this is different for home recording than it is for commercial studios. Commercial studios spend big bucks to create acoustically perfect rooms. In our world the goal is to prevent the room from having a negative impact on our projects. This can be done with the help of absorbers, bass traps, and reflectors. All of which can be made with stuff you already have of can make yourself. Example an upholstered chair or sofa makes a great bass trap when placed in the right spot. Curtains or drapes are your absorbers, and sheets of 1/4" Luan plywood can be cut and placed for reflectors. The cool thing is with some creativity you can make a decent recording space that is comfortable and looks good for not a lot of dough.
Read and research home studio building and treatments as much as you can and have a good understanding of the basics before you start stacking gear in a corner and setting up mic stands. Sticking to the tried and trued fundamentals will give you the best results in the over sound and quality of you projects. There are a lot of resources on the web. Start here with the Studio Building forum. And have fun doing it!
The only area where excess noise would be a problem is when I mic my amp (sometimes I can here my chair creeking etc.). My music is instrumental so no need to worry about vocals.