Precision Balance (1mg) vs. Analytical Balance (0.1mg) I'm in the lucky position to building my own home lab and I'm looking to get a nice balance, but I don't want to waste money on something I won't use though.

I'm currently about to start second year chemistry (Organic) and I plan to take at least a few courses beyond this as time allows (I already have my Comp Sci degree and a full time job and I've been in and out of grad school for Mathematics and Computer Science). So this is just a hobby.  As far as what I'll be doing I honestly don't know chemistry well enough to say exactly, but I think it'd be fun to synthesize various molecules you come across and see what kind of purity I could get after running the experiment a few times.

I probably won't ever get much past 4th year undergrad or 1st year graduate level knowledge since I can only take one night class at a time.

I understand that analysis and p chem have a decent amount of use for sub-mg level accuracy, but how often do these situations come up in practice?  

Should I spend the extra on a 0.1mg balance or just go for a 1mg balance?  This decision won't affect future lab purchases much more likely just the timeline of the purchases. Eventually I'd like to get additional useful instruments as I start needing them like a centrifuge and/or autoclave. But I probably won't ever get a FT-IR for example.
Either of these balances will require some care to set up. It will need to be on a solid surface away from any drafts, etc. However, neither would have the more expensive setup and maintenance requirements of say a $\pu{0.001mg}$ balance. And in either case you can take care of the cleaning and calibration yourself, particularly as it's just a hobby with no certification requirements.  

I would seriously consider looking at used equipment from a place like LabX (I have no affiliation whatsoever). I would hesitate to purchase a used $\pu{0.001mg}$ balance because that is a very sensitive piece of equipment, but a $\pu{0.1mg}$ analytical balance; my lab always bought that sort of thing used.  

You can probably get a good used $\pu{0.1mg}$ Mettler for example for the same or less than a new $\pu{1mg}$ balance and there is really no downside. It's easy to imagine you wanting to weigh out a few mg of some reagent and having the ability to do that with the extra accuracy of at least a $\pu{0.1mg}$ balance would probably be desirable.