>>1871703>There is absolutely no elevation at all on my route. There is barely any traffic and I will be going fast all the time.this logic applies equally to riding a classic groupset which you might well get a nice one of with a bike you buy to convert.
They're generally very tightly geared and suit flat fast riding. Plus at first you won't shift downtube shifters much so you can ride it with a similar mentality of just powering through in one gear.
I bought my first road bike 15 years ago to convert it to a fixie and just didn't because I liked it so much.
If you can find a beat up nice old road bike for a decent price, with horizontal dropouts, paint you like, and that fits you, it's a great idea. But don't decide if you convert it until you get it. It mostly depends on how good shape the wheels are in, if the bearing surfaces in the hubs are good and the brake tracks have life and you can get them true with evenish tension on the spokes, you should probably just overhaul it as is. But if they're shot and you can find a nice set of fixed wheels, preferable a new-ish high spec custom build someone is selling off cheap, then converting is a good idea.
The charm of either build of a nice road bike for you will be much the same. It's not that important whether it has gears or not and nor will it really affect cost.
Go prebuilt if you can't find a good classic bike.