I was going to suggest a WildLife Acoustics SM4 or SM Mini, but they will both blow your budget.
These are both passive recorders, so designed for research and monitoring. They come in a weather tight housing, that can be secured in place with a cable lock (rather like a trail camera).
The mics are omni, so pick up everything in the general area. Gain can be set at different levels, and in a quite area, you can pick up owls at a reasonable distance.
The recorders can be programmed to run at specific times, so for instance you can run a schedule from sunset to sunrise - if you set location and date correctly, the recorder will automatically determine when sunset and sunrise are!
The SM4 can be deployed in the field for a very long time, whereas the SM Mini can be deployed for over a week (dependent on temperature and memory card size).
Given your budget, something to look at may be the WildLife Acoustics SM Micro 2. The only thing to check out would be whether this is great for owls? The mic (at least on the mark 1) had a non-flat frequency response, and was most sensitive at circa 4Khz (so good for most passerines). I am not sure how sensitivity dipped at lower frequency, so you would need to understand whether recording Tawny owl hoots will be a problem. As I say, they are selling the Mk 2 now (or will do shortly), and I think the mic may have been improved.
The other downside with the micro is that is slightly less resistant to humidity, and Wildlife Acoustics suggest that you deploy it in the field with a small desiccant bag in the recorder box.
The device (as per the mini) can be setup using an app on your mobile, which makes setting the date and time, location and recording schedule easy.
WildLife Acoustics are pretty good at helping researchers, so may be worth contacting them for their opinion/confirmation, as to whether the SM Micro 2 will work.
The link to their support form is below
WA Support Form
Finally (and you are probably aware of this), from my own recording work, owls can be non vocal for very long periods. I have frequency had very intermittent calls from Tawny Owls - either hours apart, or in some cases just one vocalization in the night. I am not sure if this is because they are not very vocal, or if they have relatively large ranges. I therefore think that to ensure you capture all nearby vocals, you will need a recorder that can run through the night at least.