As soon as you are able, get yourself a proper core drill.
Core drills generally come in two forms:
1) The conventional chuck type takes a hex arbour.
2) The threaded tool holder type takes a screw fit arbour.
The former, allow you the flexibility of a standard drill. The later, the higher torque of direct drive at the expense of more laboured tool changing.
Of the chuck type the Makita 8406 is fine example, offerings from Dewalt and Bosch are marginally better, but my personal favourite is the Milwaukee DD2-160XE.
Direct drive types are the professional choice however. The Marcrist DDM2 and DDM3 are my favourites, allow wet and dry cutting at fixed speeds, and can be fitted into a drill press which allows fine control of drilling operation. I have never felt the need for variable speeds when using one of these machines, I find them remarkably efficient, particularly when paired with the same make of core cutter.
Some of my colleagues express a preference for the flexibility of variable speed control. However, when challenged on this point most admitted to leaving the drill on one particular setting for all materials, and using the limited variable speed trigger as a quasi soft-start mechanism.
Most of the major manufacturers have a range models. Hilti are the firm favourite direct drive models with most of my work mates, and these also allow wet or dry cutting.
What ever you choose to buy, don’t be tempted to use an SDS drill to drive a large core cutter. The SDS tool-holder is very inefficient when used in the hammer stop mode, a large core drill will quickly stress and wear the tool holder, causing increasing vibration and out of balance loading which will only accelerate the wear, ultimately destroying the SDS tool-holder and motor bearings in very short order.
Even the best core drills have to work extremely hard when driving large cores, the motor and drill casing can get quite hot, the best core drill motors have thermal protection to shut down the drill if the temperature becomes excessive thus preventing motor burn-out. In most cases this thermal protection is not re-settable by the operator and requires the tool to be serviced and parts replaced to restore normal operation. A notable exception are Metabo core drills which have electronic winding temperature monitoring, this system flashes a LED warning signal to the operator that the motor is approaching thermal overload.
Whether your drill has thermal protection or not, the prudent good practice if you suspect your drill of getting excessively hot, is to stop drilling, unplug, remove the core drill, reconnect, switch to the maximum speed range and run it flat out for least 5 minutes in free air to allow the motor fan to cool the windings.
All drills used for core drilling must have safety clutch, this device is vital to protect the user against the kick-back that can occur when a core jams or hits re-enforcement within the work piece.
Novices find soft-start a useful feature allowing a controlled increase in rotational speed, however, most of the current systems have a fixed acceleration which tends to err on the slow but safe principle. Experienced users often find it a time consuming nuisance and prefer to use a limited variable speed trigger as a quasi soft-start, allowing the operator to control the rate of acceleration.