PostgreSQL or MS SQL Server?

Postgres comes with pgAdmin, which does graphical explains to help you optimise queries. Entering your query in an SQL entry pane and pressing F7 gives you a really clear indication of how the query is planned and executed. More on this, here:

Graphical Explain Plans.

If you're doing a web app and are storing or working with IP Addresses, you can use the INET data type, which allows you to store the IP Address as a real type, and do all sorts of operations on it directly - Is an IP address in banned subnet, for example. No need to store 4 lots of quads and recombine them in code, or store it in a string.

Is running on Linux a bonus, if it's a .NET app?

I would consider MS SQL because of LINQ to SQL.

There is dbLinq which is still in early alpha, but it works for very simple queries.

There are a whole slew of tools for PostgreSQL, some free, some not... PgAdmin + Explain ANALYZE normally will give you everything you need and it is free.