My opinion is this. It really depends on what you are intentions are with your new knowledge.
If you intentions include (but not limited to) any of the following I would go with ASP.NET:
1) planning on creating NEW web application for production (either internally or externally) and you have the ability to choose or strongly influence the platform. Reason: you have to know what you look at in order to migrate and exisiting web application.
2) you do not plan on immediately getting into a professional develop environment but you have to time to learn and you want to spend it wisely and learn something that will be of value when you do get into a professional development. Reason: Eventhough there are some companies that have take the leap of faith and began experimenting with and in a few cases even putting into ASP.NET applications production not every company will be immediately upgrading to the .NET platform. However, as time goes on more and more companies will be migrating or in the process of migrating and will need more of this experience.
3) I eventually want to make tools for developers. Reason: as the demand grows more and more developers will be increasing the size of the .NET toolkits and your time will be more wisely spend in make tools in the .NET platform due to the increase in interest and need of the next few years.
However, if your intention include (but limited to) any of the following:
1) if you plan on providing low cost web solutions with no enterpise features (i.e. Web Services, Mobile Service). Reason: .NET is the lastest and greatest and therefore is not a cost effective solution for most businesses. I personally deal with low budget clients on a daily basis and I have try to quote a .NET solution to there problems buy they cannot afford the expense. I get a very reliable Classic ASP hosted solution with a SQL Server for as low as $75 dollars a YEAR, you can not even get .NET hosting with a SQL Server for $75 dollars a month (that I have found anyway).
2) I just want to create a family/personal site and maybe a couple of sites for my friends. Reason: .NET is intense and it just flat out would not be worth your time to learn .NET for these types of site.
Since you are familiar with other languages like ColdFusion, JSP I get the impression that you may want to lean towards the .NET platform because it on more of completitive level if not more than your current familiar languages.
.NET is not a fully tested platform just yet. I would expect there to be bugs, security issues and etc; however, because time they have spend developing this environment and because of its hype this has become Microsoft new baby. If there is bug in the environment I assure you it will get stomped on much quicker that other software packages they support.
I personnally do not believe that knowing classic ASP will be enough of an advantage to learn it first.
I hope this is of benefit to you.
Wayne Sellars
"Programming, today is a race between software developers, striving to build bigger and better idiot-proof programs, and the Universe, trying to produce bigger and better idiots. So far, Universe 1 - Programmers 0."