You wouldn't regret it!
Not sure what rent is like compared to Liverpool - do know that my dh's experience when he was divorcing was that it was chepaer to buy than to rent. That may be single bed flats though - family houses mught be different.
You'd also need to decided where you wanted to live and what about schools. SOme of the suburbs (most of the good suburbs are outside the city boundary) are very expensive. But that is not to say that there aren't aren't "good" areas within the city boundary. Down side is the high council tax - the result of the majority of the "middle classes" being outside the boundary - using our services but not paying for them).
For example, I live in the first planned (garden) suburb) in the UK - wide streets, lovely big sonte houses (most, like ours, converted into two or more houses), large gardens, beautiful parks - and all within 5 minutes of the city centre. And much better value than the over priced West End (which is also the main university area).
Harrisey might be able to advise you regarding rental, as she and her dh are moving down and renting a family home while they study.
Good things about Glasgow:
great shopping (apparently - no longer have time to go in that often);
great night life (apparently - was never one for going out, plus I was a student eslehere in Scotland and then lived in England for 9 years);
very friendly (definitely ) - my dad ran a medical conference here and go a complaint - "no-one will ever give you directions, they keep on insisting on taking you there themselves";
more parks per head pf polulation than any other city in the UK (so I beleive); world class museums (which we have to pay for out of out of our council tax - Kelvingrove, just re-opend after a c£30 million re-fit, the Burrell Collection, the Gallery of Modern Art;
close to the countryside - it's a long narrow city, so no matter where you are, you are never more than twenty minutes from the Counryside: Loch Lomond, the Trossachs and the Highlands to the North, the Ayrshire seaside to the SOuth (not all within 20 minutes!)
Good communication links - Edinburgh less than hour a away by train (50 miles by car); Easyjet form Glasgow airport, Ryanair from Prestwick
Plenty for culture vultures: Scottish Opera, Scottish Ballet, the RSNO (Royal Scottish National Orchestra), the Citizens Theatre, the Kings Theatre, the Theatre Royal.......
My dh used to "sell" Glasgow for a living (as place to move companies to), and he would probably be far more eloquent than me!