In my experience, SQL Server is a fine choice for this, and you can definitely expect better performance from SQL Server than MS-Access, with generally more optimization methods at your disposal.
I would probably go ahead and put this stuff into SQL Server Express as you've said, hopefully installed on the best machine you can use (though you did mention only 2GB of RAM). Use one table so long as it only represents one thing (I would think a pilot's flight log and a software error log wouldn't be in the same "log" table, as an absurdly contrived example). Check your performance. If it's an issue, move forward with any number of optimization techniques available to your edition of SQL Server.
Here's how I would probably do it initially:
Create your table with a non-clustered primary key, if you use a PK on your log table -- I normally use an identity column to give me a guaranteed order of events (unlike duplicate datetimes) and show possible log insert failures (missing identities). Set a clustered index on the main datetime column (you mentioned that your're already splitting into separate tables by month, so I assume you'll query this way, too). If you have a few queries that you run on this table routinely, by all means make views of them but don't expect a speedup by simply doing so. You'll more than likely want to look at indexing your table based upon the where clauses in those queries. This is where you'll be giving SQL server the information it needs to run those queries efficiently.
If you're unable to get your desired performance through optimizing your queries, indexes, using the smallest possible datatypes (especially on your indexed columns) and running on decent hardware, it may be time to try partitioned views (which require some form of ongoing maintenance) or partitioning your table. Unfortunately, SQL Server Express may limit you on what you can do with partitioning, and you'll have to decide if you need to move to a more feature-filled edition of SQL Server. You could always test partitioning with the Enterprise evaluation or Developer editions.
Update:
For the most part, I just need to filter event types and count the number.
Since past logs don't change (sort of like past sales data), storing the past aggregate numbers is an often-used strategy in this scenario. You can create a table which simply stores your counts for each month and insert new counts once a month (or week, day, etc.) with a scheduled job of some sort. Using the clustered index on your datetime column, SQL Server could much more easily aggregate the current month's numbers from the live table and add them to the stored aggregates for displaying the current values of total counts and such.