Think £99 for 2 nights is probably as good as your going to get at this stage - I sofa surf when in Edinburgh so don't know much about the hotels, etc. to be honest. Could try some of the B&Bs around Haymarket/West End (lots of fans, lots of pubs and walking distance of both Murrayfield and city centre) but I think at this stage you may struggle to get enough rooms and the quality can be a bit hit or miss.
Trains from Paisley to Glasgow to Edinburgh and onwards however, I'm one of the world's leading experts on - you don't want to know how many hours I'm forced to spend rattling around on those things!
Glasgow airport is in Paisley - about 12 miles from the city centre. There is a bus link from the airport to Paisley Gilmour Street station and then trains into Glasgow Central station - usually every 10 mins or so and take 15 mins.
The trains from Glasgow Central to Edinburgh generally take longer so best to use the Glasgow Queen Street to Edinburgh service - runs every 15 mins and takes around an hour - costs £11 (which would be each way as there are only day returns available on this service not open ones). East Coast do run a quick service from Central to Edinburgh that costs £8 each way but runs only every 2 hours (15:50, 17:50 and 19:50 on Fri eve) so would depend on your timings (need to ask for an East Coast only ticket to get the cheaper price). There is a free bus (need to show them your train ticket) from Central to Queen St running until about 8.30 I think - although it's less than a 10 min walk and easy enough to find with plenty of pubs to make pitstops in along the way. It does work out a bit cheaper to buy your tickets separately for the Paisley to Glasgow stage and the Glasgow to Edinburgh stage (and I would NEVER encourage anyone to give Scotrail a penny more than need be - they do not deserve it!)
All that said, I would just get a cab into Glasgow from the airport - use a minicab rather than a black cab - they're half the price (£12 from Paisley to the city centre - maybe pound or two more from airport but rail fare would be £3 each anyway).
http://www.renfrewshirecabco.co.uk/ are the biggest and fairly quick even if not pre-booked. Or there is a bus service from the airport to city centre, costs £7 for an open return so not really any cheaper than a cab.
If you flying to/from Glasgow, then you may want consider looking for accommodation there - think quite a few people do and you may find something cheaper at this stage than in Edinburgh. Trains from Edinburgh to Glasgow run half hourly later in the evening with the last one on Saturday's being at 11.30. It obviously won't have quite the same atmosphere as Edinburgh on Saturday night but Glasgow's still fairly good value for a night out if you wanted to continue on there - stick to Merchant City (mins walk from Queen St) or West End for the nicer venues.
Also - there's an appetizer for the match on offer in Glasgow on Friday night if you're in or passing through the city with the Blues playing the Warriors. I know they're not your team but should hopefully be a good crowd and a bit lively with plenty of visiting fans up. Firhill is about 10-15 mins walk up Maryhill Road from St George's Cross subway station. From the city centre, you'd either get the subway from Buchanan Street (adjoining Queen Street station) or St Enoch (near Central Station) - £2.40 for a return between any two stations. Cabs/hackney's from the city centre wouldn't be dear. Both Queen Street and Central have left luggage facilities if you needed them. Last train to Edinburgh is at 11.30.
