I'm probably gonna be choosing between AKG C1000s or ADK SC-1
Those are fine mics for a starting set of gear.
Mic Power- Walmoart Li-on Bat, Gain-Sp-spsb-1, storage-Nomad Jukebox 3. Id spend 100-300 on the ADC
The Walmart LiIon battery is a power
source, but not the delivery mechanism for distributing power to the mics. The SP-SB-1 will act as the delivery mechanism for power to the mics, BUT: it can't be powered by the LiIon battery, delivers plug-in power to mics via a 3.5mm stereo connector, nad the mics require phantom power via XLR connectors. So...all this to say skip the SP-SB-1, and maybe the Walmart LiIon battery depending on the power requirements for the pre/ADC you select.
The JB3, though discontinued, is a solid recording device. I'd stick with it for the moment.
With the mics you listed, plenty of budget for most of the following combos:
Mic Power | Gain | ADC
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Edirol UA5 | Edirol UA5 | Edirol UA5
Denecke PS-2 | Denecke AD-20 | Denecke AD-20
Denecke PS-2 | line transformers | Graham Patten ADC-20
Denecke DMIC-20 | Denecke DMIC-20 | Denecke DMIC-20
Sound Devices MP-2 | Sound Devices MP-2 | JB3
Sound Devices MP-2 | Sound Devices MP-2 | SBM-1
Sound Devices MP-2 | Sound Devices MP-2 | Sony D100 or M1 (replaces JB3)
Sound Devices MP-2 | Sound Devices MP-2 | modSBM-1 (a bit over your $1k budget)