Contract with the agency instead of the owner is a red flag. You want your name on a lease with the actual property owner, not an agency acting as a middleman. Ask to see proof the agency is authorised to sign on the owner's behalf, or push to deal with the owner directly.
For immigration, a signed lease works for address verification regardless of online or in person signing, but get a hard copy too.
Before signing anything, I use Lease Shield
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to check the lease for risky clauses. Free to start.