As someone who does it every day...
There are fast trains non-stop to St Pancras every 10 mins from 0618 - 0728, then roughly 2 fast trains every 15 mins (at 4/8 min intervals) until 0844. You will not get a seat on any of these after the 0658 unless it's a Friday, you stand at the back of the platform and/or you are lucky. They take 19/20 mins to St Pancras LL. Avoid the 0738 at all costs as that is the only high peak train via London Bridge and regularly leaves people behind.
To be sure of a seat get a semi-fast, calling Radlett, Elstree, Mill Hill (sometimes) and West Hampstead. These take 8 mins longer than the fasts, run every 20 mins from 0704, then 0800, 0816, 0834, 0908.
Then there are the all stations, 3 or 4 an hour, some of which start at St Abans, taking around 15 mins longer than the fasts. These are empty at St Albans. Between 30-50% of St Albans commuters take a semi-fast or slow as they would rather have a seat than 8 extra mins in bed.
Coming home it gets slightly trickier - the only way to be sure of a seat regardless of the stopping pattern is to board at Blackfriars or City, or the very front of the train at Farringdon on the second fast one of a pair 4 mins apart. Again, avoid the 1746 off St Pancras as this is the one peak London Bridge train.
12 car trains are due this December, however as there are no new trains I believe that they will only operate on the 0728, 0738 and 0800 in the morning, not sure in the pm. Given that these all have comfortably more people standing than extra seats available with 4 more cars on, there will still be standing, and of course those who currently get a slower train are more likely to migrate to them.
A tip - with 4 minute headways through the core section, when something goes wrong it goes wrong badly and quickly, particularly in the evening. For example a problem down in Brighton will stop a couple of peak trains coming through and that is enough to cause gross overcrowding. In these circumstances the best bet is to let a couple go (you won't be able to get on anyway) and get on the third or fourth train. You may not get a seat but you will be able to breathe.
By the way season tickets are not relatively cheap. Nearly £3k for 20 miles, which I think is the most expensive per mile ticket into London. If you think about doing a self-upgrade to first class, the RPIs go into first class about 1:10 trips, primarily because they physically can't get into standard. They have recently started charging twice the FC single fare to the next stop (£32 for St Albans - STP) as a penalty plus the fist class fare for the rest of the journey, rather than the £20 everyone was used to. There are a surprising number of people with first class tickets, and I don't mean free staff passes!
Finally, welcome to St Albans. The pubs are great, particularly in the older part of town.
Good luck!
