Steve/Home Energy Products will take good care of you, I have no doubt of that. He'll recommend the appropriate size unit(s) for your space, based on your needs, current insulation, other sources of air conditioning/heating, etc.
We have two 9's and an 18, the H2i HyperHeat units that excel in cooling and heating (down to some pretty chilly minus zero temps) and these units must report to individual outside units, while the standard heat pumps can share an outside unit. That could give you some additional flexibility for installation. The lines (for both types) do have max lengths and max height differences, some smaller unit minimums are 65' away, 40' rise, for larger units that increases to 100' away.
You can find all of this information in the brochures they'll give you, you can also find many online, like this one:
http://www.mehvac.com/UploadedFiles/...im_catalog.pdf
but they'll figure all that out for you. They also enclose the outside lines in a nice conduit, pictured at the end of this brochure. In some cases they can run the lines inside the wall.
With your current electric baseboard heat, you'll really see the savings, the heat pumps offer (more than!) 300% efficiency over conventional resistance/baseboard heat. A nice bonus is that like your individually zoned baseboard heat, the Mitsu's also provide zoned heating away from your oil monitor heater.
Our installation by Home Energy Products was also exceptional in every way (and I don't get to say that very often), and I'm sure they'll work with you if you have a placement concern. Our 9's are located several (5?) inches below the ceiling in the basement and master bedroom, and in the living room where we have an 18 and a cathedral ceiling, it's well balanced, but several feet under the ceiling. Regular cleaning of the air filters is needed, so the top cover/gate lifts up, hinging on the top. They'll allow room for that door to open when they install the inside unit.
There's a free iOS app that lets you take a picture (or use an existing picture) of the space you intend to install the inside unit, and it will superimpose the inside air handler. It's not perfect, but perhaps something to play with until your site visit tomorrow.
https://itunes.apple.com/us/app/meview/id461786820
They'll have plenty of photos showing past work and I have no doubt you'll have a really good sense of (everything, really) how things will look before they leave.
As far as being the new center of attention, eeh, maybe? (Measurements available in the above linked PDF) The inside units aren't especially small (I have no problem with the size relative to the function, compared to an equivalent window a/c unit). They're a nice tan color and blend in well...but as far as I'm concerned, they could have the paint scheme of a Mountain Dew soda can with flashing neon lights, because I just can't help but smile every time I see them.
I'm not alone here, look around here and off this board, everyone loves these units.
Hope you will be, too. The value these heat pumps bring (especially over supplemental electric resistance heat...+300%!!!), the reliability of the Mitsubishi product/the warrantee and the rebate too, really makes this decision a no brainer. I'm sure, if you solicit multiple quotes, there will be value/savings in the Home Energy Products bid. For us, no one was even close, and no one else told us about the rebate. They say, throw out the lowest bid, but with our offers, no one else knew the product as well as Steve from Home Energy Products in Belmont. I have no connection to them, I do not make them aware of my comments, they're just a company that took really good care of me, and I'm passing along my experience with the hope it will help others.
And come to think of it, I'm glad they're an inconspicuous tan color, I'm still smiling.
Good luck.