Inspiron models dating 2013-2015?

That would be a fourth (Haswell) or fifth (Broadwell) based system.

The Haswell would be the 3521/5521 and the Broadwell, the 5548, etc.

Once you hit the Skylake (6th generation) you're into late 2015/2016.

Once you exit the 6th generation and hit the seventh, you're into late 2016/early 2017, and you lose the option for Windows 7 (if that's a consideration);  the sixth generation is the last one that supports anything older than Windows 10.

If you're on a budget, then buying a budget PC is unlikely to be noticeably faster.  If your system currently has a traditional spinning hard drive, your cash would go much, MUCH further if you spent it on an SSD upgrade.  For everyday tasks, a five-year-old system that's been upgraded with a fast SSD will feel much faster than a brand-new system that uses a spinning hard drive, which any budget system is likely to still have.  If you use a tool like Macrium Reflect Free, you can even clone your existing drive straight over to the SSD so you don't have to rebuild your system from scratch.  Just buy a SATA to USB converter, connect the new SSD to your system temporarily with that adapter, run the clone, and then power the system off, remove the current drive, and install the SSD internally.  Done and done.

Lack of USB 3.0 unfortunately can't be solved as easily.

If you don't like the SSD idea, if you're based in the US, check out Discount Electronics.  They specialize in reselling laptops that have come off of corporate leases and such.  As a result, the prices are quite low, even though the systems you're getting are in better shape than average for their age, partly because they were used by business types, but also because they're business-class models that are built better in the first place, particularly in areas like the chassis and ESPECIALLY the quality of the keyboard.  Unfortunately, 15" business-class laptops are less common (the typical size is 14"), but there are definitely some out there, like the Latitude E55x0 series.