Ok...could you please explain what a modded unit is?
Chris Busman / Cascade Media and Oade Bros modify stock recorders. The modifications void the manufacturer's warranty, but both OB and CB/CM offer some type of warranty on the gear they mod.
Most manufacturers cut corners on the design of their recorders in order to keep costs down. One of the places they compromise on quality is the innards of the recorder, usually the analog signal path (i.e. preamp). And sometimes the analog signal path (preamp) is not designed for the type of recording we do - it's often designed for Electronic News Gathering (ENG) or some such. This sometimes results in the recorders having a gain structure that doesn't match well with our needs, e.g. inability to handle very loud sound sources (like a concert). So what does one do when a stock recorder doesn't fully satisfy one's wishes, whether in its stock design or subjective sound quality?
There are really two options available to someone if they're unhappy with the stock sound of these recorders: <1> upgrade the preamp and/or ADC by purchasing outboard gear, or <2> upgrade the recorder's own preamp / ADC by replacing the internal parts with better parts.
Typically, the CB/CM & OB modifications upgrade the analog signal path in the recorder to reduce noise, improve detail, and to some degree change the sonic signature of the stock unit. Many of us think these modded recorders sound -great-, and they're a way to achieve very high quality sound at a fraction of the cost of outboard preamps and ADCs.
As noted by others, there isn't a huge market for these modded recorders outside TS, so resale may not be as good as the outboard gear. But then again, if we all had the cash up front to buy all the outboard gear we wanted, we probably wouldn't bother with modded recorders. I look at it as a good way to get great sound on a lowish budget, not necessarily as a replacement for top-end gear that sounds great stock.
That's not to say the stock units sound terrible - they generally don't. I usually recommend someone start with a stock unit, see if they like it, and then decide later whether to have it modded.
Also as far as mics I would prefer something small that could sometimes be clipped on a hat or something. I had looked into Core Sound years ago but never bought any. Are any of those a good choice?
Adding the requirement that the mics clip to your hat will
drastically reduce your options. Most of the mics noted below are not stealthable. The only possible option noted below that I see are the AKG 391s with active ables. These are not small enough to clip to a hat, but they could be worn -in- a hat. However, you'll still have to carry the mic bodies. So you'll have the mic caps + a length of cable for each cap + the mic bodies + whatever preamp/ADC/recorder you choose (might be all-in-one, like the FR2LE and others noted already).
I'll let others speak to hat-clippable mics, as I'm not terribly familiar with them at that price point.