No it is not mandatory to have HDTV.. You can connect to normal tv also with a RCA cable which comes as the part of the package.
If you want to connect your ps3 to HDTV you need to buy an extra HDMI cable..
The console you buy depends on your preferences.. Sony has lots of features compared to xbox.. But hardware wise Sony is surely future proof.. reason being xbox has already reached it's potential.. PS3 has a blu ray drive too.. so if you are looking for total entertainment solution then you can go for PS3..
Since you don't have a HDTV which I presume.. The difference in how the game looks on xbox and ps3 won't matter.. In future if you planning to go for a HDTV (5 years) then I would highly recommend you PS3.. because the games that will be coming in next few years on PS3 will be jaw dropping as developers try to use the PS3 to it's 100%.
Regarding xbox they will surely have to come up with another device to give the current PS3 a competition in hardware..
I think that should help you decide..