Satellite systems are only expensive today because of the cost of launch -- LEO sats are in a radiation benign environment relatively speaking (vs GEO/MEO/Molniya birds which need to be rad hardened thoroughly to avoid making the next AO-10), and are relatively undemanding on their launch platform compared to higher-orbiting satellites. This means that you can pretty much use whatever decent rockets you have on hand for the job, vs needing to build a multi-stage rocket custom tailored to get into a high-velocity GTO, and reusable rocket technology is more readily applicable due to the lower deltaV needed.
Using LEO also gives you the ability to use compact terminals (see Iridium for instance) and a variety of topologies for the network (satellite buffered store-and-forward vs real-time space-to-space circuit switching vs ground interlinked satellites). The downside is you need several LEO sats to do the job of one geostationary satellite, but the much higher geostationary launch and vehicle costs can make up for it.
Ground terminals will look much like what you get with today's Iridium system in this case -- something that looks phone-like, but with a noticeable antenna vs. having one integrated into the case.
Before the development of satellites, just about all long-haul radio communications was done through HF (shortwave) radio technology, bouncing radio signals off of ionized layers of air high in Earth's atmosphere. By using sensitive receivers, frequency agility, and the knowledge and skill of operators, messages could be passed this way year-round without resorting to high-powered transmissions, and still are to this day in some parts of the world. Voice and slow-speed data are both possible, and improvements in technology have made it possible to leverage HF's strengths while mitigating its weaknesses and reducing the amount of operator intervention needed.
One thing that will be noted here is that HF is a direct, point-to-point technology -- there is no switching going on here. Stations will need to follow a protocol (such as Automatic Link Establishment) in order to find and communicate with each other, and also be able to be automatically frequency agile in order to maintain a link through ionospheric changes.
The resulting terminals will more than likely be a bit more "brick" like due to the need to supply at least a few watts of transmit power, and have long antennae, presumably an extensible whip of the type familiar from old-school transistor radios.
Meteors not only generate spectacular light shows, but ionization bursts as well. This can be used for burst-type, point-to-point links, useful for store-and-forward messaging; a system like this will be a store-and-forward switched network, presumably with some degree of peer-to-peer component to provide resiliency, as well as the ability to establish links automatically.
Generally speaking, meteor burst terminals rely on pointable, directional antennae to aid in tracking the fast-moving ionization clouds from the meteors. The resulting network would have high latency and unusual terminal designs (presumably using a phased array antenna to achieve directionality), but could be useful for emergency or command and control communications over relatively long distances.