Well having thought about it I would go with the 243 but in a good bolt action and not a cheap H&R. If that is all I could afford I would look for a good used rifle or wait and save up some more money.
In fact lets' face used is where I would be looking as new stuff I am not really impressed with.
I have a "Handi-Rifle" and it most certainly was NOT "all I could afford." In fact, the low price that these sell for here in the U.S. was something of a demerit, in my view. One simply doesn't expect such an inexpensive piece of shooting kit to deliver anything but the lowest measure of accuracy, reliability, longevity, or user satisfaction, and I was such a person -until I actually shot one, that is.
A friend of mine has a Handi-Rifle in .243 that impressed me greatly. It came from the factory with a crisp, creep-free trigger with a 3.75 pound pull weight. In shooting, I liked the fit of the stock exceptionally well and that, coupled with the decent trigger, made it a delightful rifle to shoot. It is also a very accurate one, shooting sub-MOA groups with a variety of ammo. I was so impressed that I bought a Handi-Rifle of my own, albeit in .223 instead of .243.
The Handi-Rifle actually has a lot going for it, and makes a fine stalking rifle. It is a very dynamic handling rifle, one that gets on target quickly, yet it has enough weight to allow for a steady hold under field conditions. It is compact and easy to manouver through thick hardwoods. Sure, the barrel is unpolished and blued, but it isn't very reflective because of this. It also hold paste wax well, making it a cinch to weatherproof for the severe wet weather I hunt in. That barrel sports a recessed target-type crown that was actually properly done from the factory. Mine isn't prone to copper-fouling, either, so they must have got the boring and rifling right, too.
Mine, like my friend's Handi-Rifle, is also a sub MOA grouper with a variety of loads using bullets in the 60 to 69 grain range, and is one of the few "sporting" rifles in .223 that comes with a 1:9 twist barrel. This was important to me because I use the rifle for taking light, thin skinned game up to 150 pounds or so and wanted to be able to shoot 60 grain Partitions and 62 grain TSXs accurately.
In some of the areas that I hunt, the abillity to SILENTLY unload and reload is an asset, as one must cross fences and other obsticles during the course of a stalk, and the hinge action enables one to unload and reload quickly and quietly. There is no bolt handle to snag on brush, and that is a bonus where I hunt, too.
I've owned rifles costing several times (like ten or more) what I paid for my Handi-Rifle and of all of the rifles that I've owned, my Handi-Rifle is my favorite of the lot.
The deer around my home town aren't very big and the distances they are shot at aren't very long, and for the shooting that I do here, the .223 is entirely adequate and all the cartridge that I need, assuming the use of Partitions or TSXs.
Were that not the case, and I were in the situation that the OP's friend is in, I'd buy a .243 Handi Rifle without hesitation. I would prefer that over the .25-'06 in a Handi-Rifle because the .243s have 22" barrels, whilst the .25-'06s have longer tubes that make the package less "Handi".
I like my Handi-Rifle so well, in fact, that I recently sold my CZ 550 in .30-'06 to make way for a second Handi-Rifle in that caliber.
YMMV, to each their own, and all of that, but SOME of us buy, shoot, and enjoy Handi-Rifles for reasons OTHER than their price tag.
-JP
