You'll get differing opinions on this matter, of that I'm sure
What you've got to remember is that all lumpwood is not made equal and the same goes for briquettes. You can successfully use either on a bullet smoker, using minion method or not.
Here's my opinion on both...Lumpwood Charcoal
First off, as I'm sure you know, don't touch instant lighting stuff, in an enclosed environment the lighting chemicals will taint you food. Secondly, the majority of lumpwood I've bought over here has been diabolical. It's not unusual to get a few good lumps and half a bag of slag
I've even used half a bag and then taken it back to B&Q to demand a replacement.
The safest bet with lumpwood is to go for restaurant grade if you can find it. Makro and Booker do it (in a blue bag) and it is much better than what you'll get from a garden centre or other non-trade store. This stuff comes from Bar-be-quick in Burnley, if you're near there you can buy direct from them and save about 25%
Otherwise, you can also buy direct from Big K, but you'll have to buy at least 5 bags and they don't deliver to all post codes.
Lump is fine for both normal and Minion burns. For a non minion burn I have to replenish my coals every 2-3 hours on an Excel. I'd expect the Frontier to be better though. For minion burns, don't go with the donut of unlit coals with a few lit in the middle, this is what I used to do and I was getting tainted flavors. Put a layer of unlit at the bottom of your basket and cover this with lit coals. I was shown this at last years Royal and it's definately better. This applies to briquttes too.Briquettes
This is where things get much more complicated. Briquettes are made using charcoal dust compressed and formed with binders. These binders may be as simple as vegetable starch but you never know exactly what they are
Also the ratio of fuel to binder varies from brand to brand, more binder will mean shorter burns and more ash. I find that generic supermarket briquettes have loads of binder in them, they burn up real quick and leave tons of ash. Supagrill and Big K are not too bad at all and Supagrill also do a cocoshell briquette which burns clean and long. If you're going for briquettes I'd recommend the cocoshell stuff but it's better to buy it direct from CPL as it seems to be expensive at retailers. CPL have a website, just google for it.
Overall I tend to use restaurant grade lumpwood more than anything. The best thing to do though is to try different stuff and decide for yourself what you like the best.