If you are looking for a Sam Vimes type feel then the marchers are definitely the nation for you. They are all about doing the work and getting things done. Also don’t worry about it being close to re-enactment. The wiki says that they are not about being historically accurate, even if their clothes suggested they would be. You can cast with either a wand, rod or staff. Wand being the shortest, staff being the longest. If you want to use a staff then you will have to take Magician and then battle mage. Battle mage allows you to use mage armour. This means as a mage you can wear armour as I don’t think you can wear full metal armour as a mage.
If you want to make it fairly good for combat and investigation then you can go for, shield (2 xp), Magician (2xp) and then extra spell (1xp) to allow you to take either paralysis or entangle (entangle would probably be better because even though they can still move their upper body, it is cheaper and you only start with 4 personal mana). I don’t think I need to tell you how useful a shield is. The magician skill allows you to create bonds, detect magic and operate portals.
Another thing you could do is get the magician skill, extra spell (probably with the same two options) and the battle mage skill (2xp). Now with the staff, you have the reach advantage and you will live longer with your armour.
Either way you would then have 3 xp left to spend. You could put those into lore (I recommend night, day and or winter) for rituals so you can do some detective work or you could put some into extra mana. The first rank of extra man cost 1xp and you get two extra mana, the second rank cost 2xp and again you get two extra mana.
Alternatively you could get a hero point and then either relentless or unstoppable or you could get some points in fortitude and endurance. Either of these will give you a little more survivability.
If you don’t care about viability as much and want to have a more dirty brawler then you could get the magician skill, then ambidextrous (1xp) so you can take a sword and a rod/wand. This means your enemies will have to face a crazed marcher, running at them with the furry of summer and two weapons instead of one.
You will now have 4 xp left over. Why not get the throwing skill. It is not very good but it allows you to draw throwing knives from where ever you can hide them and throw them at your unsuspecting enemy.
Now you have 3 xp. You could spend it on some of the skills I suggested above.
If you are willing to forgo the throwing knives then you would again have 4xp and so could take some skills that will have people coming to you. could pick up chirurgeon (1 xp) and then Physick will allows you to tend to peoples wounds and heal them. This could be very useful if you allies have been injured and you need to get them back up and ready to fight or if a suspect has gone down and you need them alive (though with winter magic you don’t really). It could also be a good way of getting leverage over someone in the moment. If someone is dying, you can offer to heal them for the information you want. Instead of that you could get artisan. This means you can make magical items either for yourself, for friends or for customers.
I hope I haven’t thrown out too much info and that this helps. If you don’t know about the wiki https://www.profounddecisions.co.uk/empire-wiki/Main_Page here is a link. You can find more about weapons armour and skills under rules which is the last on the right at the top.