There is a significant amount of info & recommendations on how to get best bang/buck out of insulation and how to avoid moisture traps etc on the buildingscience.com (BSC) website, but it can be tough to surf to what you actually need. There are pretty good how-to info on higher-R assemblies to be found on the greenbuildingadvisor.com website & forum too.
For new construction and full-gut rehabs I find
BSC's analysis here to be a useful starting point. Read at least the first chapter, but take note of Table 2 on page 10.
Most of Arkansas is in US climate zone 3:
http://www.greenbuildingadvisor.com/sites/default/files/images/H-T Zones with Cities ABC+.jpg
Bythe BSC analysis, according to their table, using typical methods at mid level material and labor costs, there is an economic rationale for:
R20 walls
R50 attics
R10 basement walls (if full basement or conditioned crawlspace)
R7.5 slab-edge (if slab on grade)
U0.30 windows
R5 in the center of basement or grade slabs
Above that it becomes ever harder to make it on economic arguments alone (net present value construction vs lower future energy costs), but with some DIY labor and lower cost materials, maybe. In high construction cost/low energy cost markets the crossovers are lower than that, in high energy cost/low construction cost markets you can do quite a bit better.
These are "whole assembly" values too, not center cavity. For example: A 2x6 studwall with R21 high density batts comes in at only R12-R14 after the thermal bridging of the framing is factored in. If you add 2" of rigid EPS to the exterior using 1x4 furring through-screwed to the studs with timber screws 24" o.c. (to limit thermal bridging of the fasteners) you'll be at about R20 with that 2x6 assembly. A typical 2x4 R13 wall comes in around R8.5-10 after thermal bridging, but adding 2" of rigid polyiso on the exterior brings that up to ~R20, etc.
In my area it's possible to buy reclaimed roofing foam from commercial re-roofing, which takes 60-80% of the sting out of the material cost on a foam-over. Most of it can be had at 3-4 cents per square foot per R (R10 costs 30-40 cents per square foot, f.o.b. the recycler's yard) which is cheaper than high-density batt pricing in most markets. If you're interested in going this route, call some commercial roofers in your area and ask around- many will have stockpiled pretty-good used stock in a variety of thicknesses from demolitions and re-roofing projects. Last resort you can try insulationdepot.com, but I'm not sure how close their nearest yard is to you (they have several nation wide), but will ship in truckload quantities, for price. (Local is always better, if you can.)
There is a lot of how-to tips on how to install it [URL="http://www.greenbuildingadvisor.com/blogs/dept/musings/how-install-rigid-foam-sheathing"]here[/URL], with plenty of links to blog pages going into greater detail on various aspects.
Using open cell foam or spray cellulose in the wall cavities is inherently tighter than any batt solution, but if you caulk the sheathing to the framing with acoustic sealant type caulking (including the seams between doubled top plates and between the bottom plate and subfloor, etc) you can still get pretty tight. Tight is always right- a leaky house in Arkansas has a HUGE summertime latent cooling load at any R value, and if you make it tight the interior air stays drier and more comfortable at any temperature. Air sealing is the cheapest performance upgrade you'll ever buy- if you're doing it yourself, buy a powered caulking gun that takes the bigger cartridges, and a $50 foam gun that goes onto the screw-on 1-part foam cans- it'll save a lot of time, material, and your carpal tunnels/wrists will thank you later. :-)
Air sealing & insulating basements & crawlspaces is a special topic in itself- won't go into it unless asked, but I've spelled it out for people several times on the Remodeling forum on this site in recent years.
Air sealing the upper floor ceiling plane is also critical for getting the stack-effect infiltration drives down too. If you love recessed lights, you're in for a lot of work there. If you are running ducts or air handlers in the attic it's better (but expensive) to insulate at the roof deck rather than the attic floor (there's some bang/buck issues there that can be optimized too.)
Last year I was involved in an advisory way on full-gut rehab on a friend's 3 story w/full basement circa 1905 balloon framed 2x4 house. We added 4.5" of polyiso to the exterior walls, 6" above the roof deck, all as part if a deep energy retrofit (my buddy got some subsidy from the local utility as a demonstration project, and boy did WE get schooled! :-) ) With lots of air sealing details and ridiculously tight low-U window the final air tightness came in at 464 cubic feet per minute at 50 pascals pressure (applied with a calibrated blower door.) That's about 1/10 the air tightness of a typical pretty-good house that size. Between all the measures taken the heating and cooling loads were low enough to do all heating & cooling with one mini-split heat pump per floor (!), which proved to be oversized at 1.5 tons each (I kept telling him to go with the 1-ton units at least on the lower 2 floors, but it looks like a 1-ton would handle the loads on the top floor too, but he was worried...) He did about 85-90% of the exterior foam with reclaimed goods from local recyclers, saving over ten grand in upfront cost(!).
But the result is amazing- they didn't flip the mini-splits into heating mode until November, and back in the muggy ~90F August heat they were just idling along at low speed, with the interior temps maintained at a (too cool for my liking) dry 70F. You don't have to take it nearly as far as he did to reap most of that comfort level, but this place is by far the least drafty most-comfortable place to hang in winter than any house rehab I had any part in. It's truly the case that you need to check a weather report to know if youll need a parka instead of a light sweater for stepping outs (it gets below 0F here a few times most winters)- the interior wall & window temps don't give you much of clue, and the temperatures are rock-stable.
If you insulate and air seal well enough your loads plummet, and the size/cost of mechanical systems for supporting those loads can fall too. On the rehab project I was initially thinking of using baseboard or panel radiators running off the hot water heater, but when we penciled out the heating loads and the cost of a water-heater based heating + air conditioning it seemed like a ridiculous expense for very little gain in wintertime comfort over what a ductless heat pump would provide, and in retrospect that was still the right decision. (The condensing Rinnai in the basement I'm less certain about, but hey, it works great! :-) )