Only a spate of 2? Ah, young padawan..
Whenever you get a flat, it always pays to look at the time of repair, whether roadside, pathside or at home, to help determine what caused the flat. Whilst it usually is but it's not always the tyre. It can be pinch flats to due dramatic over or under inflation, some movement of rim tape (depending on style & quality) exposing a spoke hole's sharper edge or even damage to the replacement tube by pinching with a lever by a tight tyre bead being.
However, through my riding life, my number 1 cause of repeated flats has been not properly finding and removing the cause from the tyre. Let's just say I developed better habits slowly.
Good practice is to always to install the tyre brand or logo at the valve hole. Hook the tyre back over one half of the rim wall and you can easily still rotate it around before any tube is reinstalled to line up the logo with the hole. This serves as a reference point for when the tyre is off during repair and you find an obvious (or not so obvious) hole in the tube. You hold the damaged tube up by the valve itself, or lay it down roughly as a circle with the valve being 12 o'clock. Where the known hole is in the tube, say... 3o'clock or 7 o'clock is where you go to look directly at the tyre first for any remaining glass/nail/metal shard still in the rubber.
If you don't find anything at the example 3 o'clock or 7o'clock - assume the tube was flipped and look at 9 o'clock and 5 o'clock.
If the tube puncture hole wasn't found or obvious I always still do a cursory complete check of the inside face of the tyre surface by doing a funny little routine of pressing a short section inside out with my hands for visual inspection and do a shuffling 2 handed rotation of the whole tyre feeling as much of the inner surface as possible. If you can do it in direct light, any tiny glass shard should reflect it and be obvious against the black. Hopefully you see the cause before you feel it
As for tyre choice? As others have said, it can be a religious debate... along with chain maintenance and lubrication.... and .... and ...
Not all modestly priced tyres are nasty though. Some are certainly better than others. Quality has been known to vary between production batches of the same make & model. If your budget is tight, developing a few habits and tricks, and knowing how to look for causes should still see you getting good life out of even modest tyres. Small nicks and cuts are harmless once the cause is removed. However anything that's left an obvious hole from the inside of the tyre; say anything bigger than 0.5mm should really be booted from the inside. For on the road repairs I cary a couple of folded over pieces of cloth or duct tape roughly 25 x 35mm square in my kit. Some people use $5 notes for the same purpose. Once I am home, I properly tape over the hole with a more lasting piece that's not going to move.
