If you have never shot traditional I would look for a 3 piece recurve (recurves are often easier to shoot for people new to trad than longbows) that you can buy heavier limbs for. Start at 35-40# and move up once you build up your shooting muscles. There is no let-off with trad gear so starting too heavy is a common mistake. Leave your ego at the door and start light . 3riversarchery is a good online store with lots of trad gear; bows, arrows, etc. You can check some new bows out there to get an idea. tradgang.com is a great site if you think you want to buy used.
Samick sage is a great starter and very easyy on the pocketbook. I love mine Sent from my LS670 using Tapatalk 2
3 rivers archery has a great starter pack that comes with a lot of options. It is the Samick Sage recurve. Only other thing you would need is arrows!
It depends on several things and since you're on a budget I think they become even more important. Draw Length... your draw length will effect your most effective bow length ( short draw length=shorter bow length ) This will effect smoothness of draw and affect string angle. String angle will effect string clearance on clothing. If your goal is to hunt with this bow you need to check if your state has a min. bow weight. I highly recommend contacting local Trad. archers/hunters. You'll be light years ahead of the game. I don't recommend pro-shops as very few have any knowledge about trad. equipment.. even if they act as if they do.
I would take a look at Omega Longbow. Kegan makes some fantastic shooting bows for 335$ or if your a short Draw he can make you a shortbow for around 225. Here is a link to his site. http://www.omegalongbows.webs.com/ He is fantastic to deal with and hand makes each bow to its owners specification. Finding a custom bow for this reasonable is rare. I highly recommend him.
Two good starter bows in my opinion are the Samick Sage and (if you want an offset riser which has it's own pro's and con's) the Martin Jaguar. I have shot both (and own a sage) and they are good shooters, either of which can be had for under $180.00.