Hi dddddd,
You have to set aside between 2k and 20k a month (depending on the asset class, broker and number of instruments you are going to trade) for colo and data, you can access and manage your algo from any place you want (your algo is going to run from the colo and thus is going to be at most a couple of milliseconds away from the venues). This of course if you want to actually trade at a very fast pace (directional positions) and holding periods in the order of seconds. If you are thinking about market making or pure latency or book/venue arbitrage, thats a different story, you could still do it from home :P, but the infra needed would cost you, up front, at least 400 k.
Hope this helps,
Bests,