What size unit did you buy? The biggest portable one I have seen, is around 14K btu. That is only rated for (from memory) around 600-800 square feet. If it got real hot, you would be able to cool a large room or part of a house, but not the whole thing. You generally would have to upgrade to a larger window unit for something that might do a whole house that size (24K btu for up to about 1500 square feet).
Are you planning on selling your house soon? (doesn't sound like it, since you said you expect to be in it forever) Do you have the cash to pay for it? The reasons I ask, it I would think you would want an investment, that went up in value. This would just be a home "improvement", that costs, while taking money away that could be invested. You only get the value when you sell. (until then it is a fixed asset, money pit, or a box you live in) A twenty five year old furnace, is getting close to end of life, if it is the style with electronic components. If you have one that still uses thermocouples, then you could get a lot longer out of it. (I live in an area where people still have both gravity furnaces, and 50 year old forced air furnaces)
My dream home (monolithic dome), is different in construction, so that people tend to use radiant heat and buy a window unit, because of it super insulation values (cave like), it requires about 1/2 the btu of a normal place. (cheaper to go with just a window unit, flows as well, due to fewer angles/curved structure) Where your typical box house, you would be needing fans to circulate the air to and from the window unit, or the duct work does it for a central unit. (construction verses efficiency)