You need a quad core Raspberry Pi Model 3B. These are available from several suppliers:
and many other suppliers.
The Pi needs a good power supply to provide 5.1V DC up to at least a couple of amps. It doesn't use that much current, but at boot and at other times it can draw significant current pulses. A low grade cheap supply will leave you wondering why the Pi often reboots for no apparent reason. The 6 pack of LM2596 based DC-DC converters listed below work well and you'll find other uses for them.
USB audio on the Raspberry Pi does not work properly. You have to use a daughter board (sometimes called a 'hat') if you want to do reliable audio capture. There is a stereo card made by Wolfson but it doesn't work with the quad core Pi without some modifications to the Pi operating system.
The best and perhaps the only reliable capture cards are the Audio Injector stereo and octo cards. These are made by Flatmax Studios, a small apparently one-person, company in Australia. There is a choice of two cards.
There are two versions of the stereo Audio Injector, one has a built-in microphone, go for the one listed above which doesn't have the mic.
The Octo card will enable five channel capture at 48k frames per second with 24 bit samples, and a timing jitter of some 40 nS. The stereo card will provide single channel capture at 96k samples per second with 32 bit samples and timing jitter of between 20 to 30 nS. The Pi can only run one of these cards at a time. If you want more channels, then you can use multiple Pi and Audio Injector boards and software on the Pi will synchronise the capture across them all.
There are just two major drawbacks to the Audio Injector cards. One is that there is no specification or documentation to be found anywhere. You are expected to trawl through the Forum. The other is that supply of the Octo cards is intermittent. You can usually order direct from Australia with a lead time of 3 to 4 weeks. The only other supplier appears to be Amazon USA, who are often out of stock for long periods. A minor problem with both Audio Injectors is that they don't work full duplex: you can't record and playback at the same time from independent application programs.
The GPS must be a u-blox type, based on NEO-7, LEO-7, NEO-8 or LEO-8. Try to get the NEO version if you can. The LEO needs to use an active antenna. The NEO has an extra built-in LNA so that it can use either an active or passive antenna. Apart from that, they are the same and work just as well. Both types supply DC on their antenna port to power an active antenna. You can also use a NEO-6 or LEO-6 but these are older. The 6 series only uses the GPS network. The 7 can use either GPS or GLONASS but not both at the same time. The 8 models will use satellites from GPS, GLONASS and Galileo networks, simultaneously. For ultimate performance, go for the NEO-M8T which is more expensive but is especially designed for timing applications.
There are plenty of low-cost u-blox based modules available. Choose one that has the following features:
Some typical suppliers:
You'll need to download the latest Raspbian operating system for your Pi from https://www.raspberrypi.org/downloads/raspbian/.
The full 'with desktop' version of the operating system is getting seriously bloated so download the Raspbian Stretch Lite version. You can easily add later any additional software packages that you want to use.
Follow the instructions under https://www.raspberrypi.org/documentation/installation/installing-images/README.md to copy the operating system image onto your SD card.
On your Linux workstation this is easy, use a command like
dd bs=4M if=2017-11-29-raspbian-stretch-lite.img of=/dev/sdX conv=fsync
where /dev/sdX is replaced by the device name of the SD card. Make sure you get the device name correct!!! Tail dmesg after you've plugged in the SD card to see the device name.
You may or may not need some of these depending on how you're going to box the thing.
You'll also need an enclosure to put it all in. A plastic box is sufficient and there are plenty of types to choose from. There are no controls so you don't need an instrument case. You don't need to build small and it's nice to have a bit of extra space to add things later, so guess what size box you need, then get the next size up. In fact if you're going to use the Octo then double the box size because later you'll want to fit in things like pre-amps and isolating transformers and so on.
You'll need brief temporary use of a TV or monitor with HDMI connection and a USB keyboard.
If you're still using Windows for your workstation, you'll need to install some software to be able to communicate with and use the Raspberry Pi. You'll need an X-Windows display program such as Xming and a SSH client program such as PuTTY.