For the letter from the landlord, they should specifically mention that you, as his wife, have permission to stay in the flat, and that it is big enough to accommodate the two of you. It's perfectly fine that you're not on the lease yet, as long as they mention those points specifically in their letter.
For the stuff about employment, getting a letter from his boss or the HR department is prolly the best bet, especially if he's been there two years already; sometimes the terms of the initial contract change, and the ECO wants to have the most current info available. So the letter should state the terms of his employment (full time, part time, permanent, temp, etc), how much he makes a year, how long he's been with the company, and his position in the company. My fiance didn't have his contract either, but he's been there 10 years so everything about his job has changed since then, and that's the kind of letter his HR department gave him
As to the bank statements, they don't consider printoffs from online statements to be sufficient, since those can be forged if someone was desperate enough. If he does have online bank statements, I believe he can take them into the bank and have a banker sign and stamp each page to authenticate it, unless they can provide him back statements on their letterhead (can be kinda expensive I imagine). I think this is sufficient for a spousal visa--I hope I didn't get it confused with other visas, so if I did someone will correct me
As for the courier recommendation, I haven't used any yet, so I'm sure other people can give you their personal preferences