Furniture and Fakes
Medieval displays in many museums include what is purported to be medieval furniture.
Unfortunately, that is not always the case.
What's on display in almost all second and third tier museums are reproductions ... the museum may think they're medieval, as may have the original donors, but they almost universally came with provenance equal to nothing more than 'they're old!'
First tier institutions are, at least for select key pieces, somewhat better off ... as for those (relatively few) pieces provenance exists or testing (Radiocarbon dating) has shown them to be genuine.
The only type(s) of furniture you can realistically include in your medieval dwelling is whatever may be shown in contemporary Illuminated Manuscripts ... but the accuracy of these is suspect as they either show only elite households or, where they show 'common' establishments, one has to strongly suspect they show an idealised version of the contents ... after all, their audience was the elite!
For almost all of the period Elite Households were peripatetic ... they moved from Manor to Manor, Castle to Castle, Estate to Estate every week or so (sometimes more, sometimes less).
Their destinations rarely, if ever, had much furniture beyond what was needed by the skeleton staff that maintained them between visits ... so all of the furniture and fittings needed by the elite household travelled with them. It had to be portable.
(The obvious exception was the urban elite, who were, for the most part, sedentary ... or the bulk of their household was, anyway).
So an elite household would have Folding Chairs for the Lord, his immediate family and honoured guests but Trestle Seating for the rest. Tables would almost universally be of the trestle type (or stools - which were almost always of the three legged variety)
Beds (in medieval times this meant Matresses as well) that could be taken down for the Lord, but Paliasses (or similar) which were basically bags filled with bedstraw (not Straw ... a softer and not scratchy plant) lain directly on the floor (normally covered with bundles of rushes). Very junior staff might sleep directly on the rush covered floor (modern re-enactors have found this to be quite comfortable).
Something like a Wardrobe (for hanging clothes ... not to be confused with a Wardrobe, the room(s) where clothes and other valuables were stored or the official in charge of such) might be found ... basically an upright chest. Otherwise, storage was universally in Chests ... neither Cupboards (cups, plates etc. might be displayed on shelves when not in use) nor Chests of Drawers exist ... yet.
The other thing to note is that, even in elite households, there's not a lot of furniture ... not by modern standards. Rooms are very sparse.