New thermostat and fan control

We recently acquired a 27 year old vacation home with an old but functional oil fired forced air furnace.  The thermostat is an old round Honeywell two-wire.  In this climate, the main floor can be comfortable in cool weather, but the basement room is too cool.  A heating contractor added some needed cold air return ducts in the basement and that improved things when the furnace is running.  But - there are many times when I'd like to be able to run just the furnace fan to circulate air in the house without the furnace burner running.  I'll likely hire someone to do the necessary work, but want to understand all the issues first, so here are my questions:



Obviously I have to run a new thermostat cable and want to use a modern electronic thermostat that allows me, among other things, to turn on the furnace fan at will or have it come on every now and then in "circulate mode".  With the existing thermostat, the fan is obviously controlled at the furnace end, probably by some sort of temperature sensor that detects the burner has heated up.  With the new thermostat, does the thermostat itself completely control the fan operation, and if so, is there typically some way to set the time lapse before the thermostat calls for heat and when it turns the fan on? 



Can I really expect the installer to calibrate that delay properly if that's the way the thermostat works?  Or, is there some typical fixed delay time that would be used for an oil burner and forced air installation?



On the terminal strip in the furnace, the "G" terminal (which appears to be for fan control) has no connection at present and the wiring diagram is insufficient to know why (relays are shows as outline boxes only, no contacts are shown).  To accomplish what I need, is it as straightforward as connecting this G terminal to the proper fan control terminal on the thermostat?