The Scottish political scene is rather odd when compared to the political spectrum one tends to find in independent democratic countries.
Firstly, independence rather than any other political question is the biggest political shibboleth, separating the SNP, the Greens and the SSP from Labour, the Tories and the LibDems.
Secondly, the fact that the Scottish Parliament has almost no tax-raising powers means that the parties don't divide into higher-tax-and-higher-spending parties on the left and lower-tax-and-lower-spending parties on the right. I guess the Tories are trying at times, but their message clearly doesn't appeal because they can't promise to lower any taxes.
After independence, independence will cease to be a dividing line -- I'd be very surprised if any mainstream party advocated reunification with the rUK after independence.
Furthermore, in an independent Scotland it will again be possible for a party to get votes by promising to lower taxes -- all Scandinavian countries have powerful centre-right parties, so even in a Scotland committed to the Common Weal project there will be people wanting to reduce the size of the state.
The consequence of all this is that the Scottish political landscape will most likely undergo a period of rapid change after independence.
The exact changes cannot be predicted. It's likely the SNP and Labour will continue to be the two largest parties, but it's impossible to say whether Labour will continue to be more right-wing than the SNP, or whether they'll quickly become a left-wing party again once the ties to London have been cut. Also, although I'm certain there will be a centre-right party, I'm not sure whether it will be a descendant of the Conservatives, Labour or the SNP.
This doesn't mean that Holyrood will suddenly look like Westminster. For instance, the centre-right party in an independent Scotland is likely to be a decent mildly Conservative/Liberal party more like the ones found in continental Europe rather than being dominated by lunatic Thatcherites, and left-wing parties will probably be in power more frequently than has been the case in the UK till now.
I'm definitely looking forward to Scotland becoming a normal country in this respect, too.