Don't have much experience of Ryanair, but use Easyjet regularly between Belfast and a variety of airports in the rest of the UK and France/Switzerland. Both are budget airlines and that means you have to pay for everything - mind you, internal flights in the US are much the same in that regard in my recent experience. The following comments only apply to my personal experience of EasyJet.
The key thing to remember is that you have to play by their rules or it quickly gets frantic. I have flown easyjet Belfast to Luton, Gatwick, Stansted, Glasgow, Geneva, Paris and Nice without problems. However, one viewing of the UK TV program Airline will demonstrate that if you're 5 minutes late for check-in, or have the wrong documentation, or are 5lbs over weight, they make you pay through the nose! They really are ruthless - they have to make money somewhere and it certainly isn't on the advance purchase fares! My advice is that you need to ENSURE that you will be there on time and that your discount is worth the hassle.
You need have no concerns about reliabiltity and safety. The only thing that tends to happen is that because of the quick turnarounds (approx 20 mins at the gate) they need to do to keep volume up, there is a tendency for flights later in the day to run a wee bit late. Yesterday's flight from Geneva to Belfast was cancelled due to fog in Belfast and the passengers ended up in Luton being asked to pay to get back to Belfast. That is a rare occurrence, but fog happens and easyjet claim they tried to sort the customers out (they also reneged on the charging issue after a passenger called the BBC local newsroom). In spite of all the above they also gave me a free transfer onto an earlier flight when I got into Gatwick earlier than expected on my way home from Colorado a couple of weeks ago - so I'll continue to use them!
By road, the airports you mentioned are the following distances from Heathrow: Gatwick (~44miles), Luton (~36 miles), Stansted (~66 miles). Going by road will require a trip along at least part of the infamous M25 motorway (freeway), London's orbital car park! There are bus services between the airports, but they take a while, a lot more at busy times.
An alternative, if slightly pricier mode of transport are the various express rail services to central London. The difficulty here is that they all go to different stations, so a "straight through" transfer is probably more hassle than it's worth. If you plan on spending a night in London en route, however, I would consider these.
I am intrigued by your comment about the "smaller" airports. Gatwick is London's second airport and a main hub for many UK and US carriers, including NWA, Virgin and BA. Stansted and Luton are, I agree, smaller, but substantial airports nonetheless, with a major focus on charter flights to destinations all over Europe and beyond. Heathrow can get so congested it is unreal - I avoid it when I can, although you may not have that option at this stage.
Happy to advise further if I can be of help. Keep the thread going or PM me if you'd prefer.