(2-part post):
I'm slightly worried by the fact that you say that your analogue TV reception is rather grainy. Digital TV reception usually requires a signal as good, if not better, than for analogue reception.
You might need to upgrade your aerial. The most frequently praised and recommended TV aerial, here on AB, is this one:
http://www.maplin.co.uk/Search.aspx?criteria=P T18U&DOY=15m11
However, any reputable aerial installer should be able to provide a suitable product.
Please don't let that put you off getting a digibox and trying it out. The usual guideline for assessing whether you can get digital reception is that you should be able to receive Channel 5 clearly and that the postcode checker should indicate that reception is possible. (
http://www.bbc.co.uk/digital/tv/tv_nonsubs.sht ml ). Well, I get lousy Channel 5 reception and, when I bought my box, the postcode checker said that I was outside of the Freeview area, but I still got all of the channels straight away! You won't know until you try! ;-)
I'll try to answer your question about using the box with a portable TV (which, as I read it, hasn't got a Scart socket). For that, I need to explain a bit of 'techy' stuff:
The signal which comes down your aerial is 'RF' (radio frequency). What
all digiboxes do is to decode that signal and convert it to 'AV' (audio/video). They can then feed that signal, via a Scart lead, to the TV, which simply passes it on to the screen and speakers.