Here are a couple of affordable modelling amps that i recommend for starting out, click here for more information.
Line 6 HX Stomp under £450
Line 6 are famous for their amp modelling, this uses the same sounds and technology as their flagship device, the Helix (which is my modaler of choice)! It currently features around 45 amps/cabs modeled (meaning they’re designed to sound like a specific amp as opposed to generic amp profiles on the Cube and Katana) and around 300 effects. The restriction you have is that you can only have 2 effects switches, though you can add two external switches or if you want to be clever with MIDI (I will talk about MIDI in a later blog post). I use a HX Stomp myself, for smaller gigs or for gigs where I have to travel by train and it’s portability makes it a fantastic option for practise and gigs. Like the Katana, it also features a USB out for home recording/creation of patches to save and a headphone out/aux in for scilienthome practise. If you can afford it, I highly recommend the HX Stomp.
Mooer GE 200 around £230
The Mooer GE 200 is a solid cheaper option to the HX Stomp. It actually features more amps, around 55, but unlike the Stomp which has match cabs this only has 26 cab simulations and only 70 built in effects. I also feel the amp simulation doesn’t quite live up the HX Stomp but is still to a decent standard. It also features the same USB headphone and aux functions, but the computer software isn’t as fluid as the previous two. Where it does have an advantage is that it has an onboard expression board, so you can control effects like wah, pitch (will talk about this as well in a blog post) with your foot, whereas on the Stomp you have to buy an external unit.