For my money there is only one army that fits the bill: Space Marines. They are, model per model, the baddest guys in the galaxy which thankfully means you don't need (or get to use) a lot of them. The tactical squad is flexible enough to slug it out at range or put up a very respectable fight in melee. Given that you can play an actual game with nothing more than a handful of these tac squads, they are more or less what you're looking for.
Of course, there is a downside. First, you are going to be outnumbered - this is the price that comes with having an army of superhumans clad in armor that would shame a modern main battle tank armed with weapons like chainsaws repurposed into swords and automatic weapons shooting rocket assisted explosive projectiles (and those are just the standard issue weapons). Second, the general purpose nature of the army means that you may fair poorly in a great many situations. Tau and Imperial guard quite simply outgun you and in the case of the guard can literally choke rivers with the dead for quite awhile. One can field 4o guardsmen for the price of a single tactical squad. In the case of orks, Tyranids and to an extent Chaos, you find an enemy that has superior melee potential. To face this you have litttle more than a very good chance to hit with a weapon that is fairly likely to cause a wound and the assurance that your troops will, in fact, fight to the last man (other armies have squads break when they lose a given percentage of the members).
All other armies however lose the general purpose nature. Chaos is similar to Space Marines but they trend towards the assault side of things. Worse still, Chaos generally requires more models for a given game size.
Imperial Guard require LOTS of units and trend heavily towards the ranged side of things. Oghryns and Karskin aside, most guardsmen are only useful as meaty damage absorbing armor for your tanks and other heavy weapons. Yes, they are armed, but with what is almost certainly the WORST ranged weapon in the game. The Lasrifle is utterly incapable of harming a wide number of the game's foes and even against something mundane (say an ork slugga) you'll find that a fair amount of the time should you punch through the armor you fail to deliver a wound. And, when you consider the guard can easily field the biggest army (in terms of numbers of models) I suspect you'll find it cost prohibitave as well. Worse still, the sheer size of your force, reliance on heavy weapons and the vital need to maintain the firing line means you also have an wieldy army that has difficulty reacting to unexpected changes in the battlefield.
Tau skew almost entirely to the ranged side of things. Fire Warriors, Crisis suits Etherials and the like will quickly fold under even a half-hearted assault. The Kroot provide a decent assault ability, but their addition detracts from the terrible fire that OUGHT to be pouring out from the lines at all times. The probelm here is, IF someone can close the gap, chances are quite good you'll lose the game. They also tend to require a fair investment in a number of troop types but I suspect a game can be played with the battleforce set (with runs 150 USD the last time I checked).
Orks trend heavily towards the assault side of things by simple virtue of not having many good ranged choices (and army list restrictions). Thus if you can keep them at bay for 2 or 3 turns, they are often so attritted that their assault simply washes across the line without much trouble for a guard or tau player (that is what those guardsmen are for afterall, can't scratch that new paint job on the Lemun Russ - that stuff's expensive). They tend to be numerous but seem to also be fairly cheap for most troop choices. HQ and Vehicle choices tend to be a bit expensive. I've never seen a looted Lemun Russ by itself (though I suspect it exists) and all the ork players I know (which is one guy) used an IG Lemun Russ and simply made good use of various fragments and bits to orkify it up a notch.
Tyranids again trend towards assault but do boast some impessive ranged power. Their smaller units seem to be very cheap but their large units (HQ and vehicle analogs especially) are incredibly expensive. A hive Tyrant runs 50 USD, while a Canifex (a horrible mass of armor and claws that is just shy of unkillable) is 45 USD.
Eldar are a strange mix. Individual models trend almost entirely to the assault or ranged side of things (I think even Fire Warriors would be a match for a guardian in Hand to Hand combat, while a Slugga facing a Banshee is a corpse waiting to happen), as an army they can trend either way. In general people seem to field armies with both ranged options and assault options with liberal fast attack and when orcestrated correctly this can mean you hit the enemy in their softest spots with the biggest stick. The trouble is, if the other player gains the initiave and forces you to react, your well laid plans can unravel spectacularly. It is somewhat expensive also.
A quick perusal of the Games Workshop site indicates that all the major armies have a battleforce set for around 100 USD. My advice is simply to start with one of these as it will provide a fair example for what the army will play like at a decent discount. More squads in the beginning are far from useful as it will take a few games before a player could even determine what pieces they might need or want in the future. By this standard, if I understand exchange rates properly, this works out to about 70 pounds. With the price range given you could purchse a battleforce set and one or two additional squads, assuming there are no price variations by region.
