There are four parts to a TARPN packet station: A radio link to a neighbor, a packet TNC, a Raspberry PI, and a display/control computer workstation. Let's cover each in turn.
Radios cost between $30 and $130. Link radios, the sources of same, and the connections/mods required are a subject of an ever-evolving conversation. The key is to set up a radio at your station that can talk to your neighbor station reliably, and where your neighbor has a radio on your frequency talking back. A crucial point is that one radio at your neighbor node will be dedicated to talking back to your station and to any other stations that link through your station. Every TARPN operator will buy two radios, notionally one for their end, and one for the neighbor to use to link you in. In reality we are big believers in paying it forward, so both of the radios you supply will probably remain at your house, one for your first link, and one for the ham you help get into the network (( this is a monstrous pyramid scheme!!)).
You need to consider several aspects of that including whether your you or your neighbor would get or make interference on that frequency, both to their own equipment, and to other systems. You need to coordinate baud rates, though if your link is other than 1200 baud you are probably going to be the owner of TNC, modem and radio for both ends of that link. Configuration and radio alignment are far more picky at 4800 baud and up.
The easiest link system to contemplate will make use of mono-band mobile FM ham radios, probably a used model from the 80s or 90s. This allows for frequency agility not provided by commercial 2-way radios, power not available in handie talkies, and some modicum of out-of-band interference rejection not available in modern Chinese mobile radios and HTs. 20 year old radios are OK for this application and maybe not as suitable for what they were made for because they will lack modern conveniences like fully agile PL/CTCSS encoding and remote mountable control panels. A used monoband FM ham radio mobile radio can be had for between $40 and $130 depending on the band.
Commercial radios made by Kenwood, Vertex (yeasu), Motorola, and etcetera are available for from $15 to $70 and may be much better than ham radios. The trick is in acquiring the means to channelize them and align them. Programming and alignment is much better performed in volume so either you are going to become the center for that kind of work, or you may already know such a person. The Raleigh group has specialists in different parts of that process and we've been able to utilize Kenwood and Vertex commercial synthesized radios that are 20 to 40 watts for under $50 on 51, 145 and 440Mhz. Please ask around in your area.
For the creation of your first site to site link, your neighbor may already have recommendations and a source for radios or other parts of the station. Your end could certainly make use of an already on-hand multi-mode or multi-band modern ham radio, possibly with built in TNC, but such a radio is probably expensive enough that you'll want to use it for other than packet radio. As soon as you get your packet station up and running, start shopping for replacement equipment to dedicate to packet. The nice thing about getting the system up early with the versatile radio is that now you'll better know what kind of requirements for power and antenna you are looking for when it comes time to putting new money into the hobby.
The packet radio switch is a Raspberry PI running G8BPQ node software. John Wiseman, G8BPQ, is making changes and upgrades to his package and he's been doing so since the early 90s.
The Raspberry PI costs about $50 including the memory card. We're powering it from a 12v to USB converter widget which is available for about $3. The Raspberry PI can support USB-serial TNCs as well as an I2C connected card made by Coastal Chipworks and designed in part by G8BPQ. See also TNC-PI for TARPN.
Workstation or HDMI screen
Each station needs a display and keyboard. The Raspberry PI can drive an HDMI monitor which can be a VGA monitor with the addition of a cheap adapter (see "builder" section) or a DVI monitor, also cheap adapter.
Most people will be using a Mac or MSWindows box. Linux is also just fine. The operational instructions include using any of the above.