I would avoid the bay at the moment, unless you can find a seller you personally trust. with the recent rise in popularity of straights, there is a lot of crap out there. There are a few american razor maker doing eastern style razors, so you should be able to find a good one if you look at the other popular razor forums. They are also a good place to look for good antique razors, or reviews on new ones (dovo and thier issard are ones to look at as well). Although at your price point, you would be looking at antique probably (whippeddog would be a good start). As for cost, brushes can be had fairly cheap, I would question the sanity of anyone starting out who spent more on their brush than on the blade. I've got a couple cheap antiques, but if you count in my hours spent restoring, they are quite a bit more valuable than my brush. Strops are quite reasonable, but its generally recommended to not spend a huge amount on the first one as many guys nick it while getting the hang of stropping. Again, reviews and vendors can be found on the other forums. I found that unless you have a very good supplier for leather, and work with it already, its not really economical to DIY a strop.
You should be able to get started within that 250 since you would able to find someone close by with experience and stones to hone up a razor for you (saves you the initial cost of adding to your stone collection) The very first thing you should do is get a brush and soap, and start getting used to that. That is by far one of the more important skills, and by starting with that now, you will be farther ahead when you start with the straight. Another thought, while straights are awesome, they are fiddly and time consuming. So you might want to also look into a DE (you can get a decent used or new for not too much, and blades are very cheap) That might be a good option regarding the breakouts. Change one thing at a time, and see what works. Straights are not magic, and there is quite a learning curve, so minimize your variables, and you will have much more success.