Since there appears to be advice on trains available here...
my daughter (teenage) needs to go to Brighton for the day this Saturday arriving 10am ish leaving 5pm ish. I've looked on the various websites but does anyone have any tips for a good route/ reasonable price?
It's a pity that you hadn't asked about this earlier. It would have enabled her to get a
First Capital Connect DaySave ticket. That would only cost her £12.50 (presuming Adult fare) for the Bedford to Brighton part of the journey. Together with Advance Singles (possibly to St Pancras) at £7 each way, that would have made a total fare of £26.50.
Luckily the through route under London is open this weekend and her easiest journey will be just a single change at Bedford. If she just goes along and asks for a ticket on Saturday, she will be charged £61.10 (presuming adult, half that if child).
The cheapest way would be for her to do the journey would be for her to buy a series of Off-Peak Day Return tickets:
Leicester to Kettering - £9.30
Kettering to Bedford - £9.00
Bedford to Brighton - £26.50
TOTAL £44.80
All these tickets can be bought from the ticket office at Leicester before the journey begins. She would need to travel to Bedford on a train which stops at Kettering (most, if not all, of the trains that stop at Bedford do also stop at Kettering so that is no problem)
She would then change at Bedford and catch one of the very regular direct trains from there to Brighton.
As Jeff suggests, fares will be cheaper if she has a railcard or travels in a group of 3 or 4.