Er, do not ask to view their current property. This is not standard and a good tenant will perceive you as an intrusive LL and run a mile. I would suggest best way is to make sure you do the viewings yourself and chat to them. You get a better sense of the person coupled with their financial reports than from reports alone. Ask questions, and if something is off, usually things they say won't quite add up. Estate agents don't do this because they can't tell you something doesn't feel right or they find a potential tenant "odd".
Also some tenants like to report back anything that needs maintenance (rather than necessary repair) while others don't say anything until vacating (by which a simple repair ends up causing greater damage). Some LL like to hear back every month or so about improvements, others will perceive this as the tenant trying it on/pestering. Some LL would appreciate tenants doing simple DIY repairs, others don't want their tenants to make any alterations and prefer to handle all repairs (controlling standard of work). Many conflicts in the tenant/LL arise when there's a mismatch in expectations there. When you chat with a potential tenant, you can get a sense of what they're comfortable with and see if that would work with your expectations.
perhaps consider joining the national landlords' association - nla. there is an annual fee (c. £120) but you can get quite a bit of advice from them plus template documents and discounts for services eg their tenant check. go on the website and you can find quite a bit of info. deposit needs to be protected - one scheme (if you are in england/wales) is mydepostit.co.uk - see their website for landlords' guides. we found managing agents to be a joke and decided to do it ourselves including finding tenants - saved ourselves money and headache.
Bit new to doing all this myself as to date have used agents which tbh were a complete waste of money. However, one of our tenants is leaving and they will be finding another and was wondering if anyone could recommend best way of checking references. Also what do we do about obtaining a deposit from them? Any help much appreciated. Thank you