I can confirm that artisan battlemage is very viable and works well.
I’d echo what Geoffry said about picking a good 0 mat item to start you out, but I’d have a slightly different focus in terms of items.
Your choice from the 0 material rods are heal, repel, empower or weakness.
Of these I’d personally recommend the heal option, Forlorn hope. A well placed heal is likely to have more impact on the battle than an empower, takes less set up and has the added bonus that you can heal yourself in an emergency.
Alternatively you could pick up the Hero’s girdle (0 mats, +1 hit) and use you 10 mat slot on a rod that will give you free casts. They’re mostly once per day though.
Since you mention you want to keep costs down, you could also take a wand that gives you use of one of the healing spells (dirt cheap to buy the physrep) and go into the fight with a normal weapon (assuming you have or can borrow one) and buckler and use the wand for healing.
The options for the max 10 materials item aren’t great. There are Tumultuous Gyre already mentioned, or the Quiet Word (1 free paralysis per day) in the rods section, there are some nice wands but you couldn’t bond to them at the same time as a rod. Your options are somewhat limited, although it is worth noting that you can take a second 0 material item if you want. You could always take hero’s girdle and have +1 hit whenever you didn’t have access to better armour. If you think you might pick up a staff later then there are some nice battle staffs in the 8-9 materials range.
Item 3 and 4
For the bigger items, sunfire pectoral is the classic, but don’t overlook warmages belt (11 mats free unstoppable once per day) and for the 4th slot Vambracers of regeneration (29 mats so you can’t start with them, but give you 2x free relentless per day)
A lot of this depends on what kind of battlemage you want to be. Do you want to spend your mana supporting others, supporting yourself, or killing people? There will be a certain amount of overlap but your choice really dictates which items will be most effective for you.
My main personal observation would be that in my experience the defensive mage armours had a far greater impact on my game than the offensive ones. (unless we’re talking about the really expensive options) Extra mana or an extra cast of a spell is nice, but the things kept me alive were the items that gave me the hero point abilities for free.