It is a tough decision to make, all the lathes are very good choices. I also see that the 1440GS is back in stock. There are some fairly extensive discussions on these lathe models in previous threads/postings which shed some light on the pros/cons. As parshal and GL pointed out the PM-1340GT should also be on the short list. I owned a 1340GT for about 6 years and sold it to a full time gunsmith, and have made many VFD systems for it and the 1440GT with the primary use was for gunsmiths. Both will easily turn accuracy to better than 0.001". I personally prefer Taiwanese made machines as opposed to mainland China at this price level because their quality and QC is better, very noticeable in the fit/finish. It is not all the bells and whistles, accessories that come with the machine but how well it works and the user's enjoyment of the machine. I feel the symbiosis is a bit better working with the 1340/1440GT models. You pay a premium of about 20-25% buying a Taiwanese machine, but you need to consider things like chucks that come with the machine and other components.
It does at the end of the day come down to the budget. Please be aware that the 2" spindle size is unique to the QMT lathes, I am not aware of any other manufactures lathes in the sub 10K range that offer this. I am also not aware of the standard D1-4 spindle of 1.59" being a limitation for gunsmiths unless you plan on doing very large caliber rifles. The 1340GT has a very short headstock, the 1440Gt is not much longer, which makes them both more attractive for shorter barrels. The 1340GT has a universal gearbox, but is an older open style Norton type so a bit more messy. One of my main concerns when purchasing the 1340GT was not having a foot brake, adding a VFD will give you 1-2 second braking times. My current lathe has a foot brake, but I only use it for locking the spindle for things like manual tapping. Under standard use or E-Stop I use the VFD braking which can be set to either 1 or 3 second braking. Threading, I use a proximity stop and 1 second braking, I thread at 250-450 RPM.
The 1440 BV and GS have gotten good reviews, but there have been a few QC issues. If the primary use is for gunsmithing, I probably would recommend the 3 phase 1340GT or 1440GT with a VFD. I have outlined a basic VFD install for either of these models, the VFD adds a lot of benefits in my experience in numerous installations that I have been involved with. A 3 phase motor will also give you a much better surface finish. I would estimate that of the gunsmiths buying these lathes 3/4 purchase the 1340GT and 1/4 get the 1440GT. Most add a VFD as opposed to RPC. A basic VFD install will run around $600 were you buy the components and do the install. QMT can provide some guidance documents. I have also posted some information, but I can also send you some additional information if you decide to go that route.
I think you will surprised at the end of the day how much goes into tooling/add ons for the lathe. It is easy to have 3-5K in chucks, tooling and measurement tools for the lathe, not including specialty tools for gunsmithing. Some of the measurement tooling you could pick up used either through local sales or eBay, but you need to know what you are looking for and be careful of a lot of fake measurement tools like Mitutoyo calipers. On chucks, I would suggest upgrading to the Chandox 3J Set-Tru scroll (6 or 8" sold by QMT), the Taiwanese 8" 4J independent direct mount (sold by QMT), and either a Bison/TMX 5C chcuck with collet set (sold by QMT and other vendors) or something like the Shar's ER-40 set-tru chuck and back plate for the particular lathe. You do need some form of collet holding system for small work under 1" and holding threaded rod, etc. Get a decent QCTP like the Aloris (sold by QMT) or the Dorian, tool holders buy 10-12 inexpensive ones from the vendor of you choice and save some $. You can quickly spend a lot more money when you get into boring bars, knurlers, and specialty tooling. QMT sells many items not listed on their website, best to ask if you are interested in something, or ask here and others can give their recommendations.
I would get a DRO, glass scales work fine, they all work well and are accurate. I have used the Easson DRO's on my last two lathes. You need a 1 micron slim line scale on the cross slide, this is typically the default for QMT but not other companies. The installation is not so difficult on a lathe, a good learning exercise to do your own installs but may need a mill for some of the brackets. It is important to know how to read and understand the dials and backlash on you machine and how this effects how much material is removed, the DRO helps minimize reading and counting errors. Screw up one barrel and that is the cost of the DRO. These are just tools to help you.
So back to the budget, I think you are a bit light on the numbers of what you think it is going to cost tooled up. A 1340GT tooled up as outlined with a VFD, you will probablly be in the 9-10K range.