I bought an older home in 2015.  It was partially refurbished and in good condition, but still needed a lot of work and so far I've put in about $8,500 (just materials, I didn't pay for any labor).  One problem was that there was no insulation in the crawlspace or walls, and only newly-installed R-13 in the attic.  I put about 12" of blown-in insulation in the attic and that helped, but the house still can't hold heat or cold for crap.  When it's about 30 degrees outside I can heat the house to 75 degrees with the woodstove, and the next morning it'll be down to 66 or so.  During the hotter days in the summer the AC can't quite keep up.

So, should I pay to have the walls or crawlspace insulated?  Which would make the biggest difference?  It would certainly be easier to insulate the crawlspace.

Both but with the walls being a priority.  

What year was the house built and what's the exterior veneer, vinyl siding, brick etc ?

Do you have to wear insulated slippers in the winter to walk across the floor?

The floor gets a bit cold during cold days.  It was built in 1956, and has drywall inside, with old wood siding outside with new vinyl over that.

If I were to have the walls filled with foam, how is that done?  Do they have to drill holes in the drywall for each stud space?  And then will it be possible to remove the drywall without ruining the foam?

Built in '56?
Is the electrical service actually up to date behind the drywall?
Original drywall?

Depending on the quality of the finish on the interior side of the exterior walls, I'd at least consider stripping the drywall and rewiring/insulating/drywalling with new.

In a house of '56 vintage, a house with no insulation might very well have been built in an area where code didn't require fireblocking yet, so you ought to have that installed.
If your fire code was up to date in your area in 1956, you ought have fire blocking by code in the walls which would mean that you can't just open the top of the wall and insert insulation by blow-in or foam.
One issue with the blow-in -> It settles (as much as 25%) over time, leaving gaps at the top of the walls with no insulation.
If you have fire blocking you have to blow it in at ceiling and at approx 4 feet above the floor.
Both methods require patching all the holes, and you're still stuck with 1956 wiring and fewer outlets, no cable/ethernet, etc.

Nothing is black and white, nothing is easy.

IIRC they drill a series of holes in the drywall between studs and spray it in and it expands. im not sure how well this works, it might leave dead spaces. though sounds like WAY less work intensive than pulling drywall and installing batts. Though if you do the drywall pulling route you could upgrade electricity and run ether net cable for the house, as well as do some extra wall outlets, ect ect.

It's easy to do the crawlspace yourself.

You just unroll the batts betwixt the joists and use bendy metal rods that are held up by friction (I forget the nomenclature but they'll be by the insulation at the store).  That can be done in a day or less.  It's unskilled labor so you could also pick a guy up at home depot or whatever to help bang it out quickly while you sip beer.  

The walls will make a bigger difference, but is more involved.

Are you sure there is no insulation in them already?

You can rent a blower for not too much:
http://www6.homedepot.com/tool-truck-rental/mobile/Cellulose_Insulation_Blower/118/index.html

Here's a cost calculator, as you can see labor is the most expensive part.  Yeah, you can do it yourself- check out youtube etc.  It's just drilling holes in the walls and patching.   Remember to find horizontal firebreak studs and do above and below.  This is much easier than replacing all the drywall to put Batts in.  

https://www.homewyse.com/services/cost_to_install_blown-in_wall_insulation.html

You can inject foam ( not to be confused with sprayed ) from the interior or exterior of the building assuming you have good access at the exterior.  No shrubs in the way etc..  If you do decide to open the sheetrock after the foam is installed there will be some damage but not horrible in my experiance.

It really comes down to overall cost and if you want your life disrupted on the interior of the building.  Painting and adding some electrical devices etc..

If you approach it from the exterior you're fortunate that you have vinyl siding because it can be removed and reinstalled easily.  If you had wood siding you would need to paint the exterior, additional cost.  It is important that the insulation company repairs the exterior house wrap before reinstalling the vinyl.

I researched this because parts of my house are the original 1950s construction. It has a brick veneer with cinder block behind it for the main structure the drywall is attached with furring strips.

You can't put foam behind it because the way it was built it was meant to ventilate if moisture got back there.

I've about determined the only way to insulate it will be to build a wall out from the existing wall on the inside and put in R19. I'd lose some floorspace in the room, but would have more insulation.

I also put R38 in the attic and that has helped tremendously.

My brother in law drilled holes in the drywall near the top of each stud cavity in a previous house he owned and blew in cellulose.  His neighbor unzipped some aluminum siding and did the same from the outside.  Both methods were about the same amount of work and having the insulation in the walls helped.

It's likely that you have little to no insulation in your walls.  Insulating the crawlspace won't help much if your walls aren't insulated properly.  You also probably have lots of air infiltration.  

I insulated a crawlspace with rigid foam insulation.  Worked really well and the crawlspace stayed dry and a bit above soil temps.

tag... I need to do this.. My house is terrible at holding heat, and drafty...

I have a 1956 brick rancher.  It had empty walls and aluminum windows and oil heat.  I did the blown cellulose into existing 2x4 walls myself

and paid for new vinyl windows.  The new windows and wall insulation really helped.  Gusty winds are now barely heard compared to being felt before.

I also added to the attic insulation and have a basement with concrete floor so no crawlspace to work on.

Blow in for the walls, spray foam for the crawlspace.

If your crawl space is open/vented to the sides of the house I'd recommend sealing it up, w/ a good moisture barrier and putting in a dehumidifier (google crawl space dehumidifier, about $1000). And yes, insulation. I don't think spray over bat makes a big difference if your bottling up the crawl space.

Like previously discussed you need to know how the wiring and fire blocking in the house is before you insulate. If it's already fire blocked and the wiring is up to date, then use a slow rise foam and fill the walls. If not, I'd tear down the drywall room by room, put in new romex, and fire blocking. Seal around the windows/doors with spray foam and then use bat. You really don't want to foam the walls then decide to re-wire.

Blow in cellulose.