If you don't already have a dumb trainer, then I wouldn't recommend buying one unless you can buy one really cheap from a friend or on Gumtree etc (maybe the classifieds section of this site too).
If you buy new, you'll need to pay £100 (roughly) for the dumb trainer and then another £50 for the speed sensor, for £220 you can get an entry level smart trainer...
This is the entry level smart trainer that I use (I paid £180 last year in a sale), it's a great trainer but has it's limitations (maximum sustained power of 800W and maximum simulated gradient of 6%) - neither of these limitations are a problem for people new to virtual training, in my opinion.
http://www.halfords.com/cycling/turbo-trainers/trainers/tacx-flow-t2240-smart-turbo-trainer
If you go the second hand dumb trainer route, try to get one listed on this web page - these have been tested by Zwift and will give you better results when you use them with a speed sensor:
https://zwift.com/hardware/
This is a suitable speed sensor:
https://uk.wahoofitness.com/devices/bike-sensors/bluetooth-speed-sensor
You can also get a matching cadence sensor if you want cadence data, or a two in one sensor. You only need these sensors if you use a classic/dumb trainer, but if you have Strava premium then you will be able to get more use out of them because you can use them on the road connected to your Android or iOS phone via Bluetooth (that's a premium only feature).
What device are you going to run the Zwift application on? The easiest route is to use an iPad but it will run on iPad, Mac, or PC (I think Android is coming soon).
If you use an iPad or Mac then Bluetooth is the best way to connect sensors or a smart trainer to the app, but if you use a PC then ANT+ is usually better (not all PCs support the Buetooth 4.0 standard required for these devices). For ANT+ you will need to buy a USB dongle. The speed sensor I have linked to provides data through both bluetooth and ANT+ so will work with any computer or tablet that will run Zwift.