You can use a CRT TV screen as a monitor but I advise if you want to be able to, for example read these forums with it, invest in even a cheap CRT computer monitor. There is no problem with using both a cheap monitor and a TV screen, I have that setup in my lounge room right now.
Old secondhand 15" Dell trinitron CRT and my CRT TV both hooked up to the computer.
CRT TV screens only output at a very low resolution and it can be very hard to read text off them. apart from that problem you will NEED a monitor with VGA or DVI input to set up the computer to use the video out and even to install an operating system.
As far as sound goes I'm with Costello. You seem to building a budget machine with reasonable processing power and unless I missed it you haven't mentioned what you will be outputting the sound through.
No use having an $666, 8.3 channel, DTX THC certified creato-blaster max edition soundcard if you are going to be using some cheap stereo speakers, cheap earphones or your TV speakers for the sound.
Onboard sound is very good these days and I don't know why it gets such a bad rap. I have an Audigy 2 ZS platinum pro on my main computer and it makes music sound beautiful through my expensive Sennheiser headphones and thumps my Logitech Z-680 speakers loudly. That was over AU $1200 worth all up to have that though. I would not spend that much for sound hardware again. Well the Headphones were worth every penny
But I'm a big fan of spending the money to get nice peripherals. A good quality keyboard makes more users happy with their computer than an extra 2MB of level 2 Cache ever did.
I find Monitor, Keyboard and Mouse the most important parts of the computer for MOST people. I'm sure others will reply stating that you need gigabit ethernet and water cooling but I've spent 6 years now custom building PCs for the masses and that's my experience.
Whatever you get, good luck building and I hope you are happy with what you get.