Having never owned a home before, and certainly never having had to service
a furnace before, what signs should I look for that my furnace is past the
point of serviceability and simply needs replacement? That giant cloud of
gas that forms in the basement shortly before detonation is an obvious one -
what others?

Some facts about my situation, but I guess I'm more interested about the
general case.

My particular gas furnace is approx 25 years old. It seems to heat just
fine, however its startup behavior seems weird to me.

basically, tick, tick, tick, tick, .......(about 10 seconds later) then
ignition, burners doing their stuff for about 10 seconds, blower comes on
and air starts moving. Burners shut down blower shuts down 10 to 15 seconds
later.

All of this seems normal, but I'm wondering why it takes so long for the gas
to ignite (I assume the tick, tick, tick is the sound of the igniter
sparking) and whether or not this is one of those things where you just
close you eyes and walk away.

I keep my filters clean and change it regularly.

At what point would I KNOW that this furnace is DOA and shouldn't be
repaired? At what point should I just call in the HVAC dude and have
him/her/it repair it?